Simplify -2(-4a^2+b^3)^2

$- 2 {(- 4 a^{2} + b^{3})}^{2}$

Rewrite ${(- 4 a^{2} + b^{3})}^{2}$ as $(- 4 a^{2} + b^{3}) (- 4 a^{2} + b^{3})$ .

$- 2 ((- 4 a^{2} + b^{3}) (- 4 a^{2} + b^{3}))$

Expand $(- 4 a^{2} + b^{3}) (- 4 a^{2} + b^{3})$ using the FOIL Method.

Apply the distributive property.

$- 2 (- 4 a^{2} (- 4 a^{2} + b^{3}) + b^{3} (- 4 a^{2} + b^{3}))$

Apply the distributive property.

$- 2 (- 4 a^{2} (- 4 a^{2}) - 4 a^{2} b^{3} + b^{3} (- 4 a^{2} + b^{3}))$

Apply the distributive property.

$- 2 (- 4 a^{2} (- 4 a^{2}) - 4 a^{2} b^{3} + b^{3} (- 4 a^{2}) + b^{3} b^{3})$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$- 2 (- 4 \cdot - 4 a^{2} a^{2} - 4 a^{2} b^{3} + b^{3} (- 4 a^{2}) + b^{3} b^{3})$

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

Move $a^{2}$ .

$- 2 (- 4 \cdot - 4 (a^{2} a^{2}) - 4 a^{2} b^{3} + b^{3} (- 4 a^{2}) + b^{3} b^{3})$

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

$- 2 (- 4 \cdot - 4 a^{2 + 2} - 4 a^{2} b^{3} + b^{3} (- 4 a^{2}) + b^{3} b^{3})$

Add $2$ and $2$ .

$- 2 (- 4 \cdot - 4 a^{4} - 4 a^{2} b^{3} + b^{3} (- 4 a^{2}) + b^{3} b^{3})$

Multiply $- 4$ by $- 4$ .

$- 2 (16 a^{4} - 4 a^{2} b^{3} + b^{3} (- 4 a^{2}) + b^{3} b^{3})$

Rewrite using the commutative property of multiplication.

$- 2 (16 a^{4} - 4 a^{2} b^{3} - 4 b^{3} a^{2} + b^{3} b^{3})$

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

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

$- 2 (16 a^{4} - 4 a^{2} b^{3} - 4 b^{3} a^{2} + b^{3 + 3})$

Add $3$ and $3$ .

$- 2 (16 a^{4} - 4 a^{2} b^{3} - 4 b^{3} a^{2} + b^{6})$

Subtract $4 b^{3} a^{2}$ from $- 4 a^{2} b^{3}$ .

Move $b^{3}$ .

$- 2 (16 a^{4} - 4 a^{2} b^{3} - 4 a^{2} b^{3} + b^{6})$

Subtract $4 a^{2} b^{3}$ from $- 4 a^{2} b^{3}$ .

$- 2 (16 a^{4} - 8 a^{2} b^{3} + b^{6})$

Apply the distributive property.

$- 2 (16 a^{4}) - 2 (- 8 a^{2} b^{3}) - 2 b^{6}$

Simplify.

Multiply $16$ by $- 2$ .

$- 32 a^{4} - 2 (- 8 a^{2} b^{3}) - 2 b^{6}$

Multiply $- 8$ by $- 2$ .

$- 32 a^{4} + 16 (a^{2} b^{3}) - 2 b^{6}$

Move $- 32 a^{4}$ .

$16 a^{2} b^{3} - 2 b^{6} - 32 a^{4}$

Reorder $16 a^{2} b^{3}$ and $- 2 b^{6}$ .

$- 2 b^{6} + 16 a^{2} b^{3} - 32 a^{4}$

Simplify -2(-4a^2+b^3)^2

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