Divide (12x^3-16x^2)/(2x)

$\frac{12 x^{3} - 16 x^{2}}{2 x}$

Step 1

Factor $4 x^{2}$ out of $12 x^{3} - 16 x^{2}$ .

Factor $4 x^{2}$ out of $12 x^{3}$ .

$\frac{4 x^{2} (3 x) - 16 x^{2}}{2 x}$

Factor $4 x^{2}$ out of $- 16 x^{2}$ .

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

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

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

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

Step 2

Cancel the common factor of $4$ and $2$ .

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

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

Cancel the common factors.

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Step 3

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

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

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

Cancel the common factors.

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

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

Factor $x$ out of $x^{1}$ .

$\frac{x (2 x (3 x - 4))}{x \cdot 1}$

Cancel the common factor.

$\frac{x (2 x (3 x - 4))}{x \cdot 1}$

Rewrite the expression.

$\frac{2 x (3 x - 4)}{1}$

Divide $2 x (3 x - 4)$ by $1$ .

$2 x (3 x - 4)$

$2 x (3 x - 4)$

$2 x (3 x - 4)$

Step 4

Apply the distributive property.

$2 x (3 x) + 2 x \cdot - 4$

Step 5

Rewrite using the commutative property of multiplication.

$2 \cdot 3 x \cdot x + 2 x \cdot - 4$

Step 6

Multiply $- 4$ by $2$ .

$2 \cdot 3 x \cdot x - 8 x$

Step 7

Simplify each term.

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

Move $x$ .

$2 \cdot 3 (x \cdot x) - 8 x$

Multiply $x$ by $x$ .

$2 \cdot 3 x^{2} - 8 x$

$2 \cdot 3 x^{2} - 8 x$

Multiply $2$ by $3$ .

$6 x^{2} - 8 x$

$6 x^{2} - 8 x$

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