Simplify -3ab^2(a^3b^2-2a^2b)

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

Apply the distributive property.

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

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

Move $a^{3}$ .

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

Multiply $a^{3}$ by $a$ .

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

$- 3 (a^{3} a^{1}) b^{2} b^{2} - 3 a b^{2} (- 2 a^{2} b)$

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

$- 3 a^{3 + 1} b^{2} b^{2} - 3 a b^{2} (- 2 a^{2} b)$

Add $3$ and $1$ .

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

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

Move $a^{2}$ .

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

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

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

$- 3 a^{4} b^{2} b^{2} - 3 (a^{2} a^{1}) b^{2} (- 2 b)$

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

$- 3 a^{4} b^{2} b^{2} - 3 a^{2 + 1} b^{2} (- 2 b)$

Add $2$ and $1$ .

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

Simplify each term.

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

Move $b^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

Move $b$ .

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

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

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

$- 3 a^{4} b^{4} - 3 a^{3} (b^{1} b^{2}) \cdot - 2$

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

$- 3 a^{4} b^{4} - 3 a^{3} b^{1 + 2} \cdot - 2$

Add $1$ and $2$ .

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

Multiply $- 2$ by $- 3$ .

$- 3 a^{4} b^{4} + 6 a^{3} b^{3}$