Simplify (4x^6+8x^3)/(4x^2)

$\frac{4 x^{6} + 8 x^{3}}{4 x^{2}}$

Step 1

Factor $4 x^{3}$ out of $4 x^{6} + 8 x^{3}$ .

Factor $4 x^{3}$ out of $4 x^{6}$ .

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

Factor $4 x^{3}$ out of $8 x^{3}$ .

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

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

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

Step 2

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Cancel the common factor of $x^{3}$ and $x^{2}$ .

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $x (x^{3} + 2)$ by $1$ .

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

Step 4

Apply the distributive property.

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

Step 5

Multiply $x$ by $x^{3}$ by adding the exponents.

Multiply $x$ by $x^{3}$ .

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

$x^{1} x^{3} + x \cdot 2$

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

$x^{1 + 3} + x \cdot 2$

Add $1$ and $3$ .

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

Step 6

Move $2$ to the left of $x$ .

$x^{4} + 2 x$