Simplify (-12x^4+96x^2)/(-4x)

$\frac{- 12 x^{4} + 96 x^{2}}{- 4 x}$

Step 1

Simplify terms.

Factor $12 x^{2}$ out of $- 12 x^{4} + 96 x^{2}$ .

Factor $12 x^{2}$ out of $- 12 x^{4}$ .

$\frac{12 x^{2} (- x^{2}) + 96 x^{2}}{- 4 x}$

Factor $12 x^{2}$ out of $96 x^{2}$ .

$\frac{12 x^{2} (- x^{2}) + 12 x^{2} (8)}{- 4 x}$

Factor $12 x^{2}$ out of $12 x^{2} (- x^{2}) + 12 x^{2} (8)$ .

$\frac{12 x^{2} (- x^{2} + 8)}{- 4 x}$

Cancel the common factor of $12$ and $- 4$ .

Factor $4$ out of $12 x^{2} (- x^{2} + 8)$ .

$\frac{4 (3 x^{2} (- x^{2} + 8))}{- 4 x}$

Cancel the common factors.

Factor $4$ out of $- 4 x$ .

$\frac{4 (3 x^{2} (- x^{2} + 8))}{4 (- x)}$

Cancel the common factor.

$\frac{4 (3 x^{2} (- x^{2} + 8))}{4 (- x)}$

Rewrite the expression.

$\frac{3 x^{2} (- x^{2} + 8)}{- x}$

Cancel the common factor of $x^{2}$ and $x$ .

Factor $x$ out of $3 x^{2} (- x^{2} + 8)$ .

$\frac{x (3 x (- x^{2} + 8))}{- x}$

Move the negative one from the denominator of $\frac{3 x (- x^{2} + 8)}{- 1}$ .

$- 1 \cdot (3 x (- x^{2} + 8))$

Rewrite $- 1 \cdot (3 x (- x^{2} + 8))$ as $- (3 x (- x^{2} + 8))$ .

$- (3 x (- x^{2} + 8))$

Apply the distributive property.

$- (3 x (- x^{2}) + 3 x \cdot 8)$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$- (3 \cdot - 1 x \cdot x^{2} + 3 x \cdot 8)$

Multiply $8$ by $3$ .

$- (3 \cdot - 1 x \cdot x^{2} + 24 x)$

Step 2

Simplify each term.

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

Move $x^{2}$ .

$- (3 \cdot - 1 (x^{2} x) + 24 x)$

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

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

$- (3 \cdot - 1 (x^{2} x^{1}) + 24 x)$

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

$- (3 \cdot - 1 x^{2 + 1} + 24 x)$

Add $2$ and $1$ .

$- (3 \cdot - 1 x^{3} + 24 x)$

Multiply $3$ by $- 1$ .

$- (- 3 x^{3} + 24 x)$

Step 3

Simplify by multiplying through.

Apply the distributive property.

$- (- 3 x^{3}) - (24 x)$

Multiply.

Multiply $- 3$ by $- 1$ .

$3 x^{3} - (24 x)$

Multiply $24$ by $- 1$ .

$3 x^{3} - 24 x$

Simplify (-12x^4+96x^2)/(-4x)

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