Simplify -3x^2(6x^2+2x-3)

$- 3 x^{2} (6 x^{2} + 2 x - 3)$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 3$ by $- 3$ .

$- 3 \cdot 6 x^{2} x^{2} - 3 \cdot 2 x^{2} x + 9 x^{2}$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$- 3 \cdot 6 (x^{2} x^{2}) - 3 \cdot 2 x^{2} x + 9 x^{2}$

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

$- 3 \cdot 6 x^{2 + 2} - 3 \cdot 2 x^{2} x + 9 x^{2}$

Add $2$ and $2$ .

$- 3 \cdot 6 x^{4} - 3 \cdot 2 x^{2} x + 9 x^{2}$

Multiply $- 3$ by $6$ .

$- 18 x^{4} - 3 \cdot 2 x^{2} x + 9 x^{2}$

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

Move $x$ .

$- 18 x^{4} - 3 \cdot 2 (x \cdot x^{2}) + 9 x^{2}$

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

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

$- 18 x^{4} - 3 \cdot 2 (x^{1} x^{2}) + 9 x^{2}$

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

$- 18 x^{4} - 3 \cdot 2 x^{1 + 2} + 9 x^{2}$

Add $1$ and $2$ .

$- 18 x^{4} - 3 \cdot 2 x^{3} + 9 x^{2}$

Multiply $- 3$ by $2$ .

$- 18 x^{4} - 6 x^{3} + 9 x^{2}$