Algebra Examples

$x (x - 4) (x + 5) (x - 1) = 0$

Step 1

Simplify and reorder the polynomial.

Tap for more steps...

Step 1.1

Simplify by multiplying through.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$(x \cdot x + x \cdot - 4) (x + 5) (x - 1)$

Step 1.1.2

Simplify the expression.

Tap for more steps...

Step 1.1.2.1

Multiply $x$ by $x$ .

$(x^{2} + x \cdot - 4) (x + 5) (x - 1)$

Step 1.1.2.2

Move $- 4$ to the left of $x$ .

$(x^{2} - 4 \cdot x) (x + 5) (x - 1)$

Step 1.2

Expand $(x^{2} - 4 x) (x + 5)$ using the FOIL Method.

Tap for more steps...

Step 1.2.1

Apply the distributive property.

$(x^{2} (x + 5) - 4 x (x + 5)) (x - 1)$

Step 1.2.2

Apply the distributive property.

$(x^{2} x + x^{2} \cdot 5 - 4 x (x + 5)) (x - 1)$

Step 1.2.3

Apply the distributive property.

$(x^{2} x + x^{2} \cdot 5 - 4 x \cdot x - 4 x \cdot 5) (x - 1)$

Step 1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.3.1

Simplify each term.

Tap for more steps...

Step 1.3.1.1

Multiply $x^{2}$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.3.1.1.1

Multiply $x^{2}$ by $x$ .

Tap for more steps...

Step 1.3.1.1.1.1

Raise $x$ to the power of $1$ .

$(x^{2} x^{1} + x^{2} \cdot 5 - 4 x \cdot x - 4 x \cdot 5) (x - 1)$

Step 1.3.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$(x^{2 + 1} + x^{2} \cdot 5 - 4 x \cdot x - 4 x \cdot 5) (x - 1)$

Step 1.3.1.1.2

Add $2$ and $1$ .

$(x^{3} + x^{2} \cdot 5 - 4 x \cdot x - 4 x \cdot 5) (x - 1)$

Step 1.3.1.2

Move $5$ to the left of $x^{2}$ .

$(x^{3} + 5 \cdot x^{2} - 4 x \cdot x - 4 x \cdot 5) (x - 1)$

Step 1.3.1.3

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.3.1.3.1

Move $x$ .

$(x^{3} + 5 x^{2} - 4 (x \cdot x) - 4 x \cdot 5) (x - 1)$

Step 1.3.1.3.2

Multiply $x$ by $x$ .

$(x^{3} + 5 x^{2} - 4 x^{2} - 4 x \cdot 5) (x - 1)$

Step 1.3.1.4

Multiply $5$ by $- 4$ .

$(x^{3} + 5 x^{2} - 4 x^{2} - 20 x) (x - 1)$

Step 1.3.2

Subtract $4 x^{2}$ from $5 x^{2}$ .

$(x^{3} + x^{2} - 20 x) (x - 1)$

Step 1.4

Expand $(x^{3} + x^{2} - 20 x) (x - 1)$ by multiplying each term in the first expression by each term in the second expression.

$x^{3} x + x^{3} \cdot - 1 + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5

Simplify terms.

Tap for more steps...

Step 1.5.1

Simplify each term.

Tap for more steps...

Step 1.5.1.1

Multiply $x^{3}$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.5.1.1.1

Multiply $x^{3}$ by $x$ .

Tap for more steps...

Step 1.5.1.1.1.1

Raise $x$ to the power of $1$ .

$x^{3} x^{1} + x^{3} \cdot - 1 + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{3 + 1} + x^{3} \cdot - 1 + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.1.2

Add $3$ and $1$ .

$x^{4} + x^{3} \cdot - 1 + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.2

Move $- 1$ to the left of $x^{3}$ .

$x^{4} - 1 \cdot x^{3} + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.3

Rewrite $- 1 x^{3}$ as $- x^{3}$ .

$x^{4} - x^{3} + x^{2} x + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.4

Multiply $x^{2}$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.5.1.4.1

Multiply $x^{2}$ by $x$ .

Tap for more steps...

Step 1.5.1.4.1.1

Raise $x$ to the power of $1$ .

$x^{4} - x^{3} + x^{2} x^{1} + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.4.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{4} - x^{3} + x^{2 + 1} + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.4.2

Add $2$ and $1$ .

$x^{4} - x^{3} + x^{3} + x^{2} \cdot - 1 - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.5

Move $- 1$ to the left of $x^{2}$ .

$x^{4} - x^{3} + x^{3} - 1 \cdot x^{2} - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.6

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

$x^{4} - x^{3} + x^{3} - x^{2} - 20 x \cdot x - 20 x \cdot - 1$

Step 1.5.1.7

Multiply $x$ by $x$ by adding the exponents.

Tap for more steps...

Step 1.5.1.7.1

Move $x$ .

$x^{4} - x^{3} + x^{3} - x^{2} - 20 (x \cdot x) - 20 x \cdot - 1$

Step 1.5.1.7.2

Multiply $x$ by $x$ .

$x^{4} - x^{3} + x^{3} - x^{2} - 20 x^{2} - 20 x \cdot - 1$

Step 1.5.1.8

Multiply $- 1$ by $- 20$ .

$x^{4} - x^{3} + x^{3} - x^{2} - 20 x^{2} + 20 x$

Step 1.5.2

Simplify by adding terms.

Tap for more steps...

Step 1.5.2.1

Combine the opposite terms in $x^{4} - x^{3} + x^{3} - x^{2} - 20 x^{2} + 20 x$ .

Tap for more steps...

Step 1.5.2.1.1

Add $- x^{3}$ and $x^{3}$ .

$x^{4} + 0 - x^{2} - 20 x^{2} + 20 x$

Step 1.5.2.1.2

Add $x^{4}$ and $0$ .

$x^{4} - x^{2} - 20 x^{2} + 20 x$

Step 1.5.2.2

Subtract $20 x^{2}$ from $- x^{2}$ .

$x^{4} - 21 x^{2} + 20 x$

Step 2

The largest exponent is the degree of the polynomial.

$4$