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

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $3$ by $- 2$ .

$- 2 \cdot 3 a^{2} a^{2} - 2 \cdot - 2 a^{2} a - 6 a^{2}$

Step 3

Simplify each term.

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

Move $a^{2}$ .

$- 2 \cdot 3 (a^{2} a^{2}) - 2 \cdot - 2 a^{2} a - 6 a^{2}$

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

$- 2 \cdot 3 a^{2 + 2} - 2 \cdot - 2 a^{2} a - 6 a^{2}$

Add $2$ and $2$ .

$- 2 \cdot 3 a^{4} - 2 \cdot - 2 a^{2} a - 6 a^{2}$

Multiply $- 2$ by $3$ .

$- 6 a^{4} - 2 \cdot - 2 a^{2} a - 6 a^{2}$

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

Move $a$ .

$- 6 a^{4} - 2 \cdot - 2 (a \cdot a^{2}) - 6 a^{2}$

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

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

$- 6 a^{4} - 2 \cdot - 2 (a^{1} a^{2}) - 6 a^{2}$

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

$- 6 a^{4} - 2 \cdot - 2 a^{1 + 2} - 6 a^{2}$

Add $1$ and $2$ .

$- 6 a^{4} - 2 \cdot - 2 a^{3} - 6 a^{2}$

Multiply $- 2$ by $- 2$ .

$- 6 a^{4} + 4 a^{3} - 6 a^{2}$