Simplify (-8b^3-7b^2-5)(-2b^3-2b^2-7)

$(- 8 b^{3} - 7 b^{2} - 5) (- 2 b^{3} - 2 b^{2} - 7)$

Step 1

Expand $(- 8 b^{3} - 7 b^{2} - 5) (- 2 b^{3} - 2 b^{2} - 7)$ by multiplying each term in the first expression by each term in the second expression.

$- 8 b^{3} (- 2 b^{3}) - 8 b^{3} (- 2 b^{2}) - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 8 \cdot - 2 b^{3} b^{3} - 8 b^{3} (- 2 b^{2}) - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

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

Move $b^{3}$ .

$- 8 \cdot - 2 (b^{3} b^{3}) - 8 b^{3} (- 2 b^{2}) - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

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

$- 8 \cdot - 2 b^{3 + 3} - 8 b^{3} (- 2 b^{2}) - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Add $3$ and $3$ .

$- 8 \cdot - 2 b^{6} - 8 b^{3} (- 2 b^{2}) - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $- 8$ by $- 2$ .

$16 b^{6} - 8 b^{3} (- 2 b^{2}) - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Rewrite using the commutative property of multiplication.

$16 b^{6} - 8 \cdot - 2 b^{3} b^{2} - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $b^{3}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$16 b^{6} - 8 \cdot - 2 (b^{2} b^{3}) - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

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

$16 b^{6} - 8 \cdot - 2 b^{2 + 3} - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Add $2$ and $3$ .

$16 b^{6} - 8 \cdot - 2 b^{5} - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $- 8$ by $- 2$ .

$16 b^{6} + 16 b^{5} - 8 b^{3} \cdot - 7 - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $- 7$ by $- 8$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} - 7 b^{2} (- 2 b^{3}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Rewrite using the commutative property of multiplication.

$16 b^{6} + 16 b^{5} + 56 b^{3} - 7 \cdot - 2 b^{2} b^{3} - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $b^{2}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} - 7 \cdot - 2 (b^{3} b^{2}) - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

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

$16 b^{6} + 16 b^{5} + 56 b^{3} - 7 \cdot - 2 b^{3 + 2} - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Add $3$ and $2$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} - 7 \cdot - 2 b^{5} - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $- 7$ by $- 2$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} - 7 b^{2} (- 2 b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Rewrite using the commutative property of multiplication.

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} - 7 \cdot - 2 b^{2} b^{2} - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

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

Move $b^{2}$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} - 7 \cdot - 2 (b^{2} b^{2}) - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

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

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} - 7 \cdot - 2 b^{2 + 2} - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Add $2$ and $2$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} - 7 \cdot - 2 b^{4} - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $- 7$ by $- 2$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} + 14 b^{4} - 7 b^{2} \cdot - 7 - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $- 7$ by $- 7$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} + 14 b^{4} + 49 b^{2} - 5 (- 2 b^{3}) - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $- 2$ by $- 5$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} + 14 b^{4} + 49 b^{2} + 10 b^{3} - 5 (- 2 b^{2}) - 5 \cdot - 7$

Multiply $- 2$ by $- 5$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} + 14 b^{4} + 49 b^{2} + 10 b^{3} + 10 b^{2} - 5 \cdot - 7$

Multiply $- 5$ by $- 7$ .

$16 b^{6} + 16 b^{5} + 56 b^{3} + 14 b^{5} + 14 b^{4} + 49 b^{2} + 10 b^{3} + 10 b^{2} + 35$

Simplify by adding terms.

Add $16 b^{5}$ and $14 b^{5}$ .

$16 b^{6} + 30 b^{5} + 56 b^{3} + 14 b^{4} + 49 b^{2} + 10 b^{3} + 10 b^{2} + 35$

Add $56 b^{3}$ and $10 b^{3}$ .

$16 b^{6} + 30 b^{5} + 66 b^{3} + 14 b^{4} + 49 b^{2} + 10 b^{2} + 35$

Add $49 b^{2}$ and $10 b^{2}$ .

$16 b^{6} + 30 b^{5} + 66 b^{3} + 14 b^{4} + 59 b^{2} + 35$

Move $66 b^{3}$ .

$16 b^{6} + 30 b^{5} + 14 b^{4} + 66 b^{3} + 59 b^{2} + 35$

Simplify (-8b^3-7b^2-5)(-2b^3-2b^2-7)

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