Simplify (16x^3-8x^2+4x^4)/(2x)

$\frac{16 x^{3} - 8 x^{2} + 4 x^{4}}{2 x}$

Step 1

Simplify the numerator.

Factor $4 x^{2}$ out of $16 x^{3} - 8 x^{2} + 4 x^{4}$ .

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

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

Factor $4 x^{2}$ out of $- 8 x^{2}$ .

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

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

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

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

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

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

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

Reorder terms.

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

Step 2

Simplify terms.

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

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

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

Cancel the common factors.

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2 x (x^{2} + 4 x - 2)$ by $1$ .

$2 x (x^{2} + 4 x - 2)$

Apply the distributive property.

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

Step 3

Simplify.

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 2$ by $2$ .

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

Step 4

Simplify each term.

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $4$ .

$2 x^{3} + 8 x^{2} - 4 x$

Simplify (16x^3-8x^2+4x^4)/(2x)

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