Simplify (-12x^3-48x^2)/(-4x)

$\frac{- 12 x^{3} - 48 x^{2}}{- 4 x}$

Step 1

Simplify terms.

Factor $12 x^{2}$ out of $- 12 x^{3} - 48 x^{2}$ .

Factor $12 x^{2}$ out of $- 12 x^{3}$ .

$\frac{12 x^{2} (- x) - 48 x^{2}}{- 4 x}$

Factor $12 x^{2}$ out of $- 48 x^{2}$ .

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

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

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

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $x$ out of $3 x^{2} (- x - 4)$ .

$\frac{x (3 x (- x - 4))}{- x}$

Move the negative one from the denominator of $\frac{3 x (- x - 4)}{- 1}$ .

$- 1 \cdot (3 x (- x - 4))$

Rewrite $- 1 \cdot (3 x (- x - 4))$ as $- (3 x (- x - 4))$ .

$- (3 x (- x - 4))$

Apply the distributive property.

$- (3 x (- x) + 3 x \cdot - 4)$

Simplify the expression.

Rewrite using the commutative property of multiplication.

$- (3 \cdot - 1 x \cdot x + 3 x \cdot - 4)$

Multiply $- 4$ by $3$ .

$- (3 \cdot - 1 x \cdot x - 12 x)$

Step 2

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$- (3 \cdot - 1 (x \cdot x) - 12 x)$

Multiply $x$ by $x$ .

$- (3 \cdot - 1 x^{2} - 12 x)$

Multiply $3$ by $- 1$ .

$- (- 3 x^{2} - 12 x)$

Step 3

Simplify by multiplying through.

Apply the distributive property.

$- (- 3 x^{2}) - (- 12 x)$

Multiply.

Multiply $- 3$ by $- 1$ .

$3 x^{2} - (- 12 x)$

Multiply $- 12$ by $- 1$ .

$3 x^{2} + 12 x$

Simplify (-12x^3-48x^2)/(-4x)

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