Simplify (-2ax^2+3ax-a^2)(-a^2x^2)

$(- 2 a x^{2} + 3 a x - a^{2}) (- a^{2} x^{2})$

Apply the distributive property.

$- 2 a x^{2} (- a^{2} x^{2}) + 3 a x (- a^{2} x^{2}) - a^{2} (- a^{2} x^{2})$

Simplify.

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

Move $a^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

Move $a^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

Move $a^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $- 1$ by $- 2$ .

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 1$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $- 1$ .

$2 a^{3} x^{4} - 3 a^{3} x^{3} + 1 a^{4} x^{2}$

Multiply $a^{4}$ by $1$ .

$2 a^{3} x^{4} - 3 a^{3} x^{3} + a^{4} x^{2}$

Simplify (-2ax^2+3ax-a^2)(-a^2x^2)

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