Simplify (x-5)(x^2+5x+25)

$(x - 5) (x^{2} + 5 x + 25)$

Step 1

Expand $(x - 5) (x^{2} + 5 x + 25)$ by multiplying each term in the first expression by each term in the second expression.

$x \cdot x^{2} + x (5 x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25$

Step 2

Simplify terms.

Simplify each term.

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

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

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

$x^{1} x^{2} + x (5 x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25$

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

$x^{1 + 2} + x (5 x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25$

Add $1$ and $2$ .

$x^{3} + x (5 x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25$

Rewrite using the commutative property of multiplication.

$x^{3} + 5 x \cdot x + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25$

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

Move $x$ .

$x^{3} + 5 (x \cdot x) + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25$

Multiply $x$ by $x$ .

$x^{3} + 5 x^{2} + x \cdot 25 - 5 x^{2} - 5 (5 x) - 5 \cdot 25$

Move $25$ to the left of $x$ .

$x^{3} + 5 x^{2} + 25 \cdot x - 5 x^{2} - 5 (5 x) - 5 \cdot 25$

Multiply $5$ by $- 5$ .

$x^{3} + 5 x^{2} + 25 x - 5 x^{2} - 25 x - 5 \cdot 25$

Multiply $- 5$ by $25$ .

$x^{3} + 5 x^{2} + 25 x - 5 x^{2} - 25 x - 125$

Combine the opposite terms in $x^{3} + 5 x^{2} + 25 x - 5 x^{2} - 25 x - 125$ .

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

$x^{3} + 25 x + 0 - 25 x - 125$

Add $x^{3} + 25 x$ and $0$ .

$x^{3} + 25 x - 25 x - 125$

Subtract $25 x$ from $25 x$ .

$x^{3} + 0 - 125$

Add $x^{3}$ and $0$ .

$x^{3} - 125$