Simplify (a+5)(a^2-7a+7)

$(a + 5) (a^{2} - 7 a + 7)$

Step 1

Expand $(a + 5) (a^{2} - 7 a + 7)$ by multiplying each term in the first expression by each term in the second expression.

$a \cdot a^{2} + a (- 7 a) + a \cdot 7 + 5 a^{2} + 5 (- 7 a) + 5 \cdot 7$

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 $1$ .

$a^{1} a^{2} + a (- 7 a) + a \cdot 7 + 5 a^{2} + 5 (- 7 a) + 5 \cdot 7$

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

$a^{1 + 2} + a (- 7 a) + a \cdot 7 + 5 a^{2} + 5 (- 7 a) + 5 \cdot 7$

Add $1$ and $2$ .

$a^{3} + a (- 7 a) + a \cdot 7 + 5 a^{2} + 5 (- 7 a) + 5 \cdot 7$

Rewrite using the commutative property of multiplication.

$a^{3} - 7 a \cdot a + a \cdot 7 + 5 a^{2} + 5 (- 7 a) + 5 \cdot 7$

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

Move $a$ .

$a^{3} - 7 (a \cdot a) + a \cdot 7 + 5 a^{2} + 5 (- 7 a) + 5 \cdot 7$

Multiply $a$ by $a$ .

$a^{3} - 7 a^{2} + a \cdot 7 + 5 a^{2} + 5 (- 7 a) + 5 \cdot 7$

Move $7$ to the left of $a$ .

$a^{3} - 7 a^{2} + 7 \cdot a + 5 a^{2} + 5 (- 7 a) + 5 \cdot 7$

Multiply $- 7$ by $5$ .

$a^{3} - 7 a^{2} + 7 a + 5 a^{2} - 35 a + 5 \cdot 7$

Multiply $5$ by $7$ .

$a^{3} - 7 a^{2} + 7 a + 5 a^{2} - 35 a + 35$

Simplify by adding terms.

Add $- 7 a^{2}$ and $5 a^{2}$ .

$a^{3} - 2 a^{2} + 7 a - 35 a + 35$

Subtract $35 a$ from $7 a$ .

$a^{3} - 2 a^{2} - 28 a + 35$