Cálculo Ejemplos

$f (x) = {(3 x^{2} - 1)}^{2}$

Paso 1

Considera la fórmula del cociente diferencial.

$\frac{f (x + h) - f (x)}{h}$

Paso 2

Obtén los componentes de la definición.

Toca para ver más pasos...

Paso 2.1

Evalúa la función en $x = x + h$ .

Toca para ver más pasos...

Paso 2.1.1

Reemplaza la variable $x$ con $x + h$ en la expresión.

$f (x + h) = {(3 {(x + h)}^{2} - 1)}^{2}$

Paso 2.1.2

Simplifica el resultado.

Toca para ver más pasos...

Paso 2.1.2.1

Simplifica los términos.

Toca para ver más pasos...

Paso 2.1.2.1.1

Simplifica cada término.

Toca para ver más pasos...

Paso 2.1.2.1.1.1

Reescribe ${(x + h)}^{2}$ como $(x + h) (x + h)$ .

$f (x + h) = {(3 ((x + h) (x + h)) - 1)}^{2}$

Paso 2.1.2.1.1.2

Expande $(x + h) (x + h)$ con el método PEIU (primero, exterior, interior, ultimo).

Toca para ver más pasos...

Paso 2.1.2.1.1.2.1

Aplica la propiedad distributiva.

$f (x + h) = {(3 (x (x + h) + h (x + h)) - 1)}^{2}$

Paso 2.1.2.1.1.2.2

Aplica la propiedad distributiva.

$f (x + h) = {(3 (x \cdot x + x h + h (x + h)) - 1)}^{2}$

Paso 2.1.2.1.1.2.3

Aplica la propiedad distributiva.

$f (x + h) = {(3 (x \cdot x + x h + h x + h \cdot h) - 1)}^{2}$

Paso 2.1.2.1.1.3

Simplifica y combina los términos similares.

Toca para ver más pasos...

Paso 2.1.2.1.1.3.1

Simplifica cada término.

Toca para ver más pasos...

Paso 2.1.2.1.1.3.1.1

Multiplica $x$ por $x$ .

$f (x + h) = {(3 (x^{2} + x h + h x + h \cdot h) - 1)}^{2}$

Paso 2.1.2.1.1.3.1.2

Multiplica $h$ por $h$ .

$f (x + h) = {(3 (x^{2} + x h + h x + h^{2}) - 1)}^{2}$

Paso 2.1.2.1.1.3.2

Suma $x h$ y $h x$ .

Toca para ver más pasos...

Paso 2.1.2.1.1.3.2.1

Reordena $x$ y $h$ .

$f (x + h) = {(3 (x^{2} + h x + h x + h^{2}) - 1)}^{2}$

Paso 2.1.2.1.1.3.2.2

Suma $h x$ y $h x$ .

$f (x + h) = {(3 (x^{2} + 2 h x + h^{2}) - 1)}^{2}$

Paso 2.1.2.1.1.4

Aplica la propiedad distributiva.

$f (x + h) = {(3 x^{2} + 3 (2 h x) + 3 h^{2} - 1)}^{2}$

Paso 2.1.2.1.1.5

Multiplica $2$ por $3$ .

$f (x + h) = {(3 x^{2} + 6 h x + 3 h^{2} - 1)}^{2}$

Paso 2.1.2.1.2

Reescribe ${(3 x^{2} + 6 h x + 3 h^{2} - 1)}^{2}$ como $(3 x^{2} + 6 h x + 3 h^{2} - 1) (3 x^{2} + 6 h x + 3 h^{2} - 1)$ .

$f (x + h) = (3 x^{2} + 6 h x + 3 h^{2} - 1) (3 x^{2} + 6 h x + 3 h^{2} - 1)$

Paso 2.1.2.2

Expande $(3 x^{2} + 6 h x + 3 h^{2} - 1) (3 x^{2} + 6 h x + 3 h^{2} - 1)$ mediante la multiplicación de cada término de la primera expresión por cada término de la segunda expresión.

$f (x + h) = 3 x^{2} (3 x^{2}) + 3 x^{2} (6 h x) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3

Simplifica cada término.

Toca para ver más pasos...

Paso 2.1.2.3.1

Reescribe con la propiedad conmutativa de la multiplicación.

$f (x + h) = 3 \cdot (3 x^{2} x^{2}) + 3 x^{2} (6 h x) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.2

Multiplica $x^{2}$ por $x^{2}$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.1.2.3.2.1

Mueve $x^{2}$ .

$f (x + h) = 3 \cdot (3 (x^{2} x^{2})) + 3 x^{2} (6 h x) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$f (x + h) = 3 \cdot (3 x^{2 + 2}) + 3 x^{2} (6 h x) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.2.3

Suma $2$ y $2$ .

$f (x + h) = 3 \cdot (3 x^{4}) + 3 x^{2} (6 h x) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.3

Multiplica $3$ por $3$ .

$f (x + h) = 9 x^{4} + 3 x^{2} (6 h x) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.4

Multiplica $x^{2}$ por $x$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.1.2.3.4.1

Mueve $x$ .

$f (x + h) = 9 x^{4} + 3 (x \cdot x^{2}) (6 h) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.4.2

Multiplica $x$ por $x^{2}$ .

Toca para ver más pasos...

Paso 2.1.2.3.4.2.1

Eleva $x$ a la potencia de $1$ .

Paso 2.1.2.3.4.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$f (x + h) = 9 x^{4} + 3 x^{1 + 2} (6 h) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.4.3

Suma $1$ y $2$ .

$f (x + h) = 9 x^{4} + 3 x^{3} (6 h) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.5

Reescribe con la propiedad conmutativa de la multiplicación.

$f (x + h) = 9 x^{4} + 3 \cdot (6 x^{3} h) + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.6

Multiplica $3$ por $6$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 3 x^{2} (3 h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.7

Reescribe con la propiedad conmutativa de la multiplicación.

$f (x + h) = 9 x^{4} + 18 x^{3} h + 3 \cdot (3 x^{2} h^{2}) + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.8

Multiplica $3$ por $3$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} + 3 x^{2} \cdot - 1 + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.9

Multiplica $- 1$ por $3$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 6 h x (3 x^{2}) + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.10

Multiplica $x$ por $x^{2}$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.1.2.3.10.1

Mueve $x^{2}$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 6 h (x^{2} x) \cdot 3 + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.10.2

Multiplica $x^{2}$ por $x$ .

Toca para ver más pasos...

Paso 2.1.2.3.10.2.1

Eleva $x$ a la potencia de $1$ .

Paso 2.1.2.3.10.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 6 h x^{2 + 1} \cdot 3 + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.10.3

Suma $2$ y $1$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 6 h x^{3} \cdot 3 + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.11

Multiplica $3$ por $6$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 6 h x (6 h x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.12

Multiplica $h$ por $h$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.1.2.3.12.1

Mueve $h$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 6 (h \cdot h) x (6 x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.12.2

Multiplica $h$ por $h$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 6 h^{2} x (6 x) + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.13

Multiplica $x$ por $x$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.1.2.3.13.1

Mueve $x$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 6 h^{2} (x \cdot x) \cdot 6 + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.13.2

Multiplica $x$ por $x$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 6 h^{2} x^{2} \cdot 6 + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.14

Multiplica $6$ por $6$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 6 h x (3 h^{2}) + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.15

Multiplica $h$ por $h^{2}$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.1.2.3.15.1

Mueve $h^{2}$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 6 (h^{2} h) x \cdot 3 + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.15.2

Multiplica $h^{2}$ por $h$ .

Toca para ver más pasos...

Paso 2.1.2.3.15.2.1

Eleva $h$ a la potencia de $1$ .

Paso 2.1.2.3.15.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 6 h^{2 + 1} x \cdot 3 + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.15.3

Suma $2$ y $1$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 6 h^{3} x \cdot 3 + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.16

Multiplica $3$ por $6$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x + 6 h x \cdot - 1 + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.17

Multiplica $- 1$ por $6$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 3 h^{2} (3 x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.18

Reescribe con la propiedad conmutativa de la multiplicación.

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 3 \cdot (3 h^{2} x^{2}) + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.19

Multiplica $3$ por $3$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 3 h^{2} (6 h x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.20

Multiplica $h^{2}$ por $h$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.1.2.3.20.1

Mueve $h$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 3 (h \cdot h^{2}) (6 x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.20.2

Multiplica $h$ por $h^{2}$ .

Toca para ver más pasos...

Paso 2.1.2.3.20.2.1

Eleva $h$ a la potencia de $1$ .

Paso 2.1.2.3.20.2.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 3 h^{1 + 2} (6 x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.20.3

Suma $1$ y $2$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 3 h^{3} (6 x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.21

Reescribe con la propiedad conmutativa de la multiplicación.

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 3 \cdot (6 h^{3} x) + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.22

Multiplica $3$ por $6$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 3 h^{2} (3 h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.23

Reescribe con la propiedad conmutativa de la multiplicación.

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 3 \cdot (3 h^{2} h^{2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.24

Multiplica $h^{2}$ por $h^{2}$ sumando los exponentes.

Toca para ver más pasos...

Paso 2.1.2.3.24.1

Mueve $h^{2}$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 3 \cdot (3 (h^{2} h^{2})) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.24.2

Usa la regla de la potencia $a^{m} a^{n} = a^{m + n}$ para combinar exponentes.

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 3 \cdot (3 h^{2 + 2}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.24.3

Suma $2$ y $2$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 3 \cdot (3 h^{4}) + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.25

Multiplica $3$ por $3$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} + 3 h^{2} \cdot - 1 - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.26

Multiplica $- 1$ por $3$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 1 (3 x^{2}) - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.27

Multiplica $3$ por $- 1$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 3 x^{2} - 1 (6 h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.28

Multiplica $6$ por $- 1$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 3 x^{2} - 6 (h x) - 1 (3 h^{2}) - 1 \cdot - 1$

Paso 2.1.2.3.29

Multiplica $3$ por $- 1$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 3 x^{2} - 6 h x - 3 h^{2} - 1 \cdot - 1$

Paso 2.1.2.3.30

Multiplica $- 1$ por $- 1$ .

$f (x + h) = 9 x^{4} + 18 x^{3} h + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 3 x^{2} - 6 h x - 3 h^{2} + 1$

Paso 2.1.2.4

Suma $18 x^{3} h$ y $18 h x^{3}$ .

Toca para ver más pasos...

Paso 2.1.2.4.1

Mueve $x^{3}$ .

$f (x + h) = 9 x^{4} + 9 x^{2} h^{2} - 3 x^{2} + 18 h x^{3} + 18 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 3 x^{2} - 6 h x - 3 h^{2} + 1$

Paso 2.1.2.4.2

Suma $18 h x^{3}$ y $18 h x^{3}$ .

$f (x + h) = 9 x^{4} + 9 x^{2} h^{2} - 3 x^{2} + 36 h x^{3} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 3 x^{2} - 6 h x - 3 h^{2} + 1$

Paso 2.1.2.5

Suma $9 x^{2} h^{2}$ y $36 h^{2} x^{2}$ .

Toca para ver más pasos...

Paso 2.1.2.5.1

Mueve $x^{2}$ .

$f (x + h) = 9 x^{4} - 3 x^{2} + 36 h x^{3} + 9 h^{2} x^{2} + 36 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 3 x^{2} - 6 h x - 3 h^{2} + 1$

Paso 2.1.2.5.2

Suma $9 h^{2} x^{2}$ y $36 h^{2} x^{2}$ .

$f (x + h) = 9 x^{4} - 3 x^{2} + 36 h x^{3} + 45 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 3 x^{2} - 6 h x - 3 h^{2} + 1$

Paso 2.1.2.6

Resta $3 x^{2}$ de $- 3 x^{2}$ .

$f (x + h) = 9 x^{4} - 6 x^{2} + 36 h x^{3} + 45 h^{2} x^{2} + 18 h^{3} x - 6 h x + 9 h^{2} x^{2} + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 6 h x - 3 h^{2} + 1$

Paso 2.1.2.7

Suma $45 h^{2} x^{2}$ y $9 h^{2} x^{2}$ .

$f (x + h) = 9 x^{4} - 6 x^{2} + 36 h x^{3} + 54 h^{2} x^{2} + 18 h^{3} x - 6 h x + 18 h^{3} x + 9 h^{4} - 3 h^{2} - 6 h x - 3 h^{2} + 1$

Paso 2.1.2.8

Suma $18 h^{3} x$ y $18 h^{3} x$ .

$f (x + h) = 9 x^{4} - 6 x^{2} + 36 h x^{3} + 54 h^{2} x^{2} + 36 h^{3} x - 6 h x + 9 h^{4} - 3 h^{2} - 6 h x - 3 h^{2} + 1$

Paso 2.1.2.9

Resta $6 h x$ de $- 6 h x$ .

$f (x + h) = 9 x^{4} - 6 x^{2} + 36 h x^{3} + 54 h^{2} x^{2} + 36 h^{3} x + 9 h^{4} - 3 h^{2} - 12 h x - 3 h^{2} + 1$

Paso 2.1.2.10

Resta $3 h^{2}$ de $- 3 h^{2}$ .

$f (x + h) = 9 x^{4} - 6 x^{2} + 36 h x^{3} + 54 h^{2} x^{2} + 36 h^{3} x + 9 h^{4} - 6 h^{2} - 12 h x + 1$

Paso 2.1.2.11

La respuesta final es $9 x^{4} - 6 x^{2} + 36 h x^{3} + 54 h^{2} x^{2} + 36 h^{3} x + 9 h^{4} - 6 h^{2} - 12 h x + 1$ .

$9 x^{4} - 6 x^{2} + 36 h x^{3} + 54 h^{2} x^{2} + 36 h^{3} x + 9 h^{4} - 6 h^{2} - 12 h x + 1$

Paso 2.2

Reordena.

Toca para ver más pasos...

Paso 2.2.1

Mueve $- 6 x^{2}$ .

$9 x^{4} + 36 h x^{3} + 54 h^{2} x^{2} + 36 h^{3} x + 9 h^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1$

Paso 2.2.2

Mueve $9 x^{4}$ .

$36 h x^{3} + 54 h^{2} x^{2} + 36 h^{3} x + 9 h^{4} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1$

Paso 2.2.3

Mueve $36 h x^{3}$ .

$54 h^{2} x^{2} + 36 h^{3} x + 9 h^{4} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1$

Paso 2.2.4

Mueve $54 h^{2} x^{2}$ .

$36 h^{3} x + 9 h^{4} + 54 h^{2} x^{2} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1$

Paso 2.2.5

Reordena $36 h^{3} x$ y $9 h^{4}$ .

$9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1$

Paso 2.3

Obtén los componentes de la definición.

$f (x + h) = 9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1$

$f (x) = 9 x^{4} - 6 x^{2} + 1$

$f (x + h) = 9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1$

$f (x) = 9 x^{4} - 6 x^{2} + 1$

Paso 3

Inserta los componentes.

$\frac{f (x + h) - f (x)}{h} = \frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1 - (9 x^{4} - 6 x^{2} + 1)}{h}$

Paso 4

Simplifica.

Toca para ver más pasos...

Paso 4.1

Simplifica el numerador.

Toca para ver más pasos...

Paso 4.1.1

Aplica la propiedad distributiva.

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1 - (9 x^{4}) - (- 6 x^{2}) - 1 \cdot 1}{h}$

Paso 4.1.2

Simplifica.

Toca para ver más pasos...

Paso 4.1.2.1

Multiplica $9$ por $- 1$ .

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1 - 9 x^{4} - (- 6 x^{2}) - 1 \cdot 1}{h}$

Paso 4.1.2.2

Multiplica $- 6$ por $- 1$ .

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1 - 9 x^{4} + 6 x^{2} - 1 \cdot 1}{h}$

Paso 4.1.2.3

Multiplica $- 1$ por $1$ .

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} + 9 x^{4} - 6 h^{2} - 12 h x - 6 x^{2} + 1 - 9 x^{4} + 6 x^{2} - 1}{h}$

Paso 4.1.3

Resta $9 x^{4}$ de $9 x^{4}$ .

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x - 6 x^{2} + 1 + 0 + 6 x^{2} - 1}{h}$

Paso 4.1.4

Suma $9 h^{4}$ y $0$ .

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x - 6 x^{2} + 1 + 6 x^{2} - 1}{h}$

Paso 4.1.5

Suma $- 6 x^{2}$ y $6 x^{2}$ .

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x + 0 + 1 - 1}{h}$

Paso 4.1.6

Suma $9 h^{4}$ y $0$ .

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x + 1 - 1}{h}$

Paso 4.1.7

Resta $1$ de $1$ .

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x + 0}{h}$

Paso 4.1.8

Suma $9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x$ y $0$ .

$\frac{9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x}{h}$

Paso 4.1.9

Factoriza $3 h$ de $9 h^{4} + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x$ .

Toca para ver más pasos...

Paso 4.1.9.1

Factoriza $3 h$ de $9 h^{4}$ .

$\frac{3 h (3 h^{3}) + 36 h^{3} x + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x}{h}$

Paso 4.1.9.2

Factoriza $3 h$ de $36 h^{3} x$ .

$\frac{3 h (3 h^{3}) + 3 h (12 h^{2} x) + 54 h^{2} x^{2} + 36 h x^{3} - 6 h^{2} - 12 h x}{h}$

Paso 4.1.9.3

Factoriza $3 h$ de $54 h^{2} x^{2}$ .

$\frac{3 h (3 h^{3}) + 3 h (12 h^{2} x) + 3 h (18 h x^{2}) + 36 h x^{3} - 6 h^{2} - 12 h x}{h}$

Paso 4.1.9.4

Factoriza $3 h$ de $36 h x^{3}$ .

$\frac{3 h (3 h^{3}) + 3 h (12 h^{2} x) + 3 h (18 h x^{2}) + 3 h (12 x^{3}) - 6 h^{2} - 12 h x}{h}$

Paso 4.1.9.5

Factoriza $3 h$ de $- 6 h^{2}$ .

$\frac{3 h (3 h^{3}) + 3 h (12 h^{2} x) + 3 h (18 h x^{2}) + 3 h (12 x^{3}) + 3 h (- 2 h) - 12 h x}{h}$

Paso 4.1.9.6

Factoriza $3 h$ de $- 12 h x$ .

$\frac{3 h (3 h^{3}) + 3 h (12 h^{2} x) + 3 h (18 h x^{2}) + 3 h (12 x^{3}) + 3 h (- 2 h) + 3 h (- 4 x)}{h}$

Paso 4.1.9.7

Factoriza $3 h$ de $3 h (3 h^{3}) + 3 h (12 h^{2} x)$ .

$\frac{3 h (3 h^{3} + 12 h^{2} x) + 3 h (18 h x^{2}) + 3 h (12 x^{3}) + 3 h (- 2 h) + 3 h (- 4 x)}{h}$

Paso 4.1.9.8

Factoriza $3 h$ de $3 h (3 h^{3} + 12 h^{2} x) + 3 h (18 h x^{2})$ .

$\frac{3 h (3 h^{3} + 12 h^{2} x + 18 h x^{2}) + 3 h (12 x^{3}) + 3 h (- 2 h) + 3 h (- 4 x)}{h}$

Paso 4.1.9.9

Factoriza $3 h$ de $3 h (3 h^{3} + 12 h^{2} x + 18 h x^{2}) + 3 h (12 x^{3})$ .

$\frac{3 h (3 h^{3} + 12 h^{2} x + 18 h x^{2} + 12 x^{3}) + 3 h (- 2 h) + 3 h (- 4 x)}{h}$

Paso 4.1.9.10

Factoriza $3 h$ de $3 h (3 h^{3} + 12 h^{2} x + 18 h x^{2} + 12 x^{3}) + 3 h (- 2 h)$ .

$\frac{3 h (3 h^{3} + 12 h^{2} x + 18 h x^{2} + 12 x^{3} - 2 h) + 3 h (- 4 x)}{h}$

Paso 4.1.9.11

Factoriza $3 h$ de $3 h (3 h^{3} + 12 h^{2} x + 18 h x^{2} + 12 x^{3} - 2 h) + 3 h (- 4 x)$ .

$\frac{3 h (3 h^{3} + 12 h^{2} x + 18 h x^{2} + 12 x^{3} - 2 h - 4 x)}{h}$

Paso 4.2

Simplifica los términos.

Toca para ver más pasos...

Paso 4.2.1

Cancela el factor común de $h$ .

Toca para ver más pasos...

Paso 4.2.1.1

Cancela el factor común.

$\frac{3 h (3 h^{3} + 12 h^{2} x + 18 h x^{2} + 12 x^{3} - 2 h - 4 x)}{h}$

Paso 4.2.1.2

Divide $3 (3 h^{3} + 12 h^{2} x + 18 h x^{2} + 12 x^{3} - 2 h - 4 x)$ por $1$ .

$3 (3 h^{3} + 12 h^{2} x + 18 h x^{2} + 12 x^{3} - 2 h - 4 x)$

Paso 4.2.2

Aplica la propiedad distributiva.

$3 (3 h^{3}) + 3 (12 h^{2} x) + 3 (18 h x^{2}) + 3 (12 x^{3}) + 3 (- 2 h) + 3 (- 4 x)$

Paso 4.3

Simplifica.

Toca para ver más pasos...

Paso 4.3.1

Multiplica $3$ por $3$ .

$9 h^{3} + 3 (12 h^{2} x) + 3 (18 h x^{2}) + 3 (12 x^{3}) + 3 (- 2 h) + 3 (- 4 x)$

Paso 4.3.2

Multiplica $12$ por $3$ .

$9 h^{3} + 36 (h^{2} x) + 3 (18 h x^{2}) + 3 (12 x^{3}) + 3 (- 2 h) + 3 (- 4 x)$

Paso 4.3.3

Multiplica $18$ por $3$ .

$9 h^{3} + 36 (h^{2} x) + 54 (h x^{2}) + 3 (12 x^{3}) + 3 (- 2 h) + 3 (- 4 x)$

Paso 4.3.4

Multiplica $12$ por $3$ .

$9 h^{3} + 36 (h^{2} x) + 54 (h x^{2}) + 36 x^{3} + 3 (- 2 h) + 3 (- 4 x)$

Paso 4.3.5

Multiplica $- 2$ por $3$ .

$9 h^{3} + 36 (h^{2} x) + 54 (h x^{2}) + 36 x^{3} - 6 h + 3 (- 4 x)$

Paso 4.3.6

Multiplica $- 4$ por $3$ .

$9 h^{3} + 36 (h^{2} x) + 54 (h x^{2}) + 36 x^{3} - 6 h - 12 x$

Paso 4.4

Elimina los paréntesis.

$9 h^{3} + 36 h^{2} x + 54 h x^{2} + 36 x^{3} - 6 h - 12 x$

Paso 4.5

Simplifica la expresión.

Toca para ver más pasos...

Paso 4.5.1

Mueve $h^{2}$ .

$9 h^{3} + 36 x h^{2} + 54 h x^{2} + 36 x^{3} - 6 h - 12 x$

Paso 4.5.2

Mueve $h$ .

$9 h^{3} + 36 x h^{2} + 54 x^{2} h + 36 x^{3} - 6 h - 12 x$

Paso 4.5.3

Mueve $- 6 h$ .

$9 h^{3} + 36 x h^{2} + 54 x^{2} h + 36 x^{3} - 12 x - 6 h$

Paso 4.5.4

Mueve $9 h^{3}$ .

$36 x h^{2} + 54 x^{2} h + 36 x^{3} + 9 h^{3} - 12 x - 6 h$

Paso 4.5.5

Mueve $36 x h^{2}$ .

$54 x^{2} h + 36 x^{3} + 36 x h^{2} + 9 h^{3} - 12 x - 6 h$

Paso 4.5.6

Reordena $54 x^{2} h$ y $36 x^{3}$ .

$36 x^{3} + 54 x^{2} h + 36 x h^{2} + 9 h^{3} - 12 x - 6 h$

Paso 5