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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

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

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

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

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

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

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

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a$ .

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

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

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

Multiply $5$ by $- 5$ .

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

Multiply $- 5$ by $25$ .

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

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

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

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

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

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

Subtract $25 a$ from $25 a$ .

$a^{3} + 0 - 125$

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

$a^{3} - 125$