Álgebra Ejemplos

$12 a x^{2} - 20 c y^{2} - 18 b x^{2} - 10 a y^{2} + 15 b y^{2} + 24 c x^{2}$

Paso 1

Reagrupa los términos.

$- 20 c y^{2} - 10 a y^{2} + 12 a x^{2} - 18 b x^{2} + 15 b y^{2} + 24 c x^{2}$

Paso 2

Factoriza $- 10 y^{2}$ de $- 20 c y^{2} - 10 a y^{2}$ .

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Paso 2.1

Reordena $- 20 c y^{2}$ y $- 10 a y^{2}$ .

$- 10 a y^{2} - 20 c y^{2} + 12 a x^{2} - 18 b x^{2} + 15 b y^{2} + 24 c x^{2}$

Paso 2.2

Factoriza $- 10 y^{2}$ de $- 10 a y^{2}$ .

$- 10 y^{2} (a) - 20 c y^{2} + 12 a x^{2} - 18 b x^{2} + 15 b y^{2} + 24 c x^{2}$

Paso 2.3

Factoriza $- 10 y^{2}$ de $- 20 c y^{2}$ .

$- 10 y^{2} (a) - 10 y^{2} (2 c) + 12 a x^{2} - 18 b x^{2} + 15 b y^{2} + 24 c x^{2}$

Paso 2.4

Factoriza $- 10 y^{2}$ de $- 10 y^{2} (a) - 10 y^{2} (2 c)$ .

$- 10 y^{2} (a + 2 c) + 12 a x^{2} - 18 b x^{2} + 15 b y^{2} + 24 c x^{2}$

Paso 3

Factoriza $3$ de $12 a x^{2} - 18 b x^{2} + 15 b y^{2} + 24 c x^{2}$ .

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Paso 3.1

Factoriza $3$ de $12 a x^{2}$ .

$- 10 y^{2} (a + 2 c) + 3 (4 a x^{2}) - 18 b x^{2} + 15 b y^{2} + 24 c x^{2}$

Paso 3.2

Factoriza $3$ de $- 18 b x^{2}$ .

$- 10 y^{2} (a + 2 c) + 3 (4 a x^{2}) + 3 (- 6 b x^{2}) + 15 b y^{2} + 24 c x^{2}$

Paso 3.3

Factoriza $3$ de $15 b y^{2}$ .

$- 10 y^{2} (a + 2 c) + 3 (4 a x^{2}) + 3 (- 6 b x^{2}) + 3 (5 b y^{2}) + 24 c x^{2}$

Paso 3.4

Factoriza $3$ de $24 c x^{2}$ .

$- 10 y^{2} (a + 2 c) + 3 (4 a x^{2}) + 3 (- 6 b x^{2}) + 3 (5 b y^{2}) + 3 (8 c x^{2})$

Paso 3.5

Factoriza $3$ de $3 (4 a x^{2}) + 3 (- 6 b x^{2})$ .

$- 10 y^{2} (a + 2 c) + 3 (4 a x^{2} - 6 b x^{2}) + 3 (5 b y^{2}) + 3 (8 c x^{2})$

Paso 3.6

Factoriza $3$ de $3 (4 a x^{2} - 6 b x^{2}) + 3 (5 b y^{2})$ .

$- 10 y^{2} (a + 2 c) + 3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2}) + 3 (8 c x^{2})$

Paso 3.7

Factoriza $3$ de $3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2}) + 3 (8 c x^{2})$ .

$- 10 y^{2} (a + 2 c) + 3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2} + 8 c x^{2})$

Paso 4

Factoriza $- 1$ de $- 10 y^{2} (a + 2 c) + 3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2} + 8 c x^{2})$ .

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Paso 4.1

Reordena $- 10 y^{2} (a + 2 c)$ y $3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2} + 8 c x^{2})$ .

$3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2} + 8 c x^{2}) - 10 y^{2} (a + 2 c)$

Paso 4.2

Factoriza $- 1$ de $3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2} + 8 c x^{2})$ .

$- (- 3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2} + 8 c x^{2})) - 10 y^{2} (a + 2 c)$

Paso 4.3

Factoriza $- 1$ de $- 10 y^{2} (a + 2 c)$ .

$- (- 3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2} + 8 c x^{2})) - (10 y^{2} (a + 2 c))$

Paso 4.4

Factoriza $- 1$ de $- (- 3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2} + 8 c x^{2})) - (10 y^{2} (a + 2 c))$ .

$- (- 3 (4 a x^{2} - 6 b x^{2} + 5 b y^{2} + 8 c x^{2}) + 10 y^{2} (a + 2 c))$

Paso 5

Aplica la propiedad distributiva.

$- (- 3 (4 a x^{2}) - 3 (- 6 b x^{2}) - 3 (5 b y^{2}) - 3 (8 c x^{2}) + 10 y^{2} (a + 2 c))$

Paso 6

Simplifica.

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Paso 6.1

Multiplica $4$ por $- 3$ .

$- (- 12 (a x^{2}) - 3 (- 6 b x^{2}) - 3 (5 b y^{2}) - 3 (8 c x^{2}) + 10 y^{2} (a + 2 c))$

Paso 6.2

Multiplica $- 6$ por $- 3$ .

$- (- 12 (a x^{2}) + 18 (b x^{2}) - 3 (5 b y^{2}) - 3 (8 c x^{2}) + 10 y^{2} (a + 2 c))$

Paso 6.3

Multiplica $5$ por $- 3$ .

$- (- 12 (a x^{2}) + 18 (b x^{2}) - 15 (b y^{2}) - 3 (8 c x^{2}) + 10 y^{2} (a + 2 c))$

Paso 6.4

Multiplica $8$ por $- 3$ .

$- (- 12 (a x^{2}) + 18 (b x^{2}) - 15 (b y^{2}) - 24 (c x^{2}) + 10 y^{2} (a + 2 c))$

Paso 7

Simplifica cada término.

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Paso 7.1

Elimina los paréntesis.

$- (- 12 a x^{2} + 18 (b x^{2}) - 15 (b y^{2}) - 24 (c x^{2}) + 10 y^{2} (a + 2 c))$

Paso 7.2

Elimina los paréntesis.

$- (- 12 a x^{2} + 18 b x^{2} - 15 (b y^{2}) - 24 (c x^{2}) + 10 y^{2} (a + 2 c))$

Paso 7.3

Elimina los paréntesis.

$- (- 12 a x^{2} + 18 b x^{2} - 15 b y^{2} - 24 (c x^{2}) + 10 y^{2} (a + 2 c))$

Paso 7.4

Elimina los paréntesis.

$- (- 12 a x^{2} + 18 b x^{2} - 15 b y^{2} - 24 c x^{2} + 10 y^{2} (a + 2 c))$

Paso 8

Aplica la propiedad distributiva.

$- (- 12 a x^{2} + 18 b x^{2} - 15 b y^{2} - 24 c x^{2} + 10 y^{2} a + 10 y^{2} (2 c))$

Paso 9

Reescribe con la propiedad conmutativa de la multiplicación.

$- (- 12 a x^{2} + 18 b x^{2} - 15 b y^{2} - 24 c x^{2} + 10 y^{2} a + 10 \cdot 2 y^{2} c)$

Paso 10

Multiplica $10$ por $2$ .

$- (- 12 a x^{2} + 18 b x^{2} - 15 b y^{2} - 24 c x^{2} + 10 y^{2} a + 20 y^{2} c)$