Algebra Examples

$(5 x^{4} y^{2} + 20 x y^{6} - 10 x) \div 5 x y^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{5 x^{4} y^{2} + 20 x y^{6} - 10 x}{5 x y^{2}}$

Step 2

Factor $5 x$ out of $5 x^{4} y^{2} + 20 x y^{6} - 10 x$ .

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Step 2.1

Factor $5 x$ out of $5 x^{4} y^{2}$ .

$\frac{5 x (x^{3} y^{2}) + 20 x y^{6} - 10 x}{5 x y^{2}}$

Step 2.2

Factor $5 x$ out of $20 x y^{6}$ .

$\frac{5 x (x^{3} y^{2}) + 5 x (4 y^{6}) - 10 x}{5 x y^{2}}$

Step 2.3

Factor $5 x$ out of $- 10 x$ .

$\frac{5 x (x^{3} y^{2}) + 5 x (4 y^{6}) + 5 x (- 2)}{5 x y^{2}}$

Step 2.4

Factor $5 x$ out of $5 x (x^{3} y^{2}) + 5 x (4 y^{6})$ .

$\frac{5 x (x^{3} y^{2} + 4 y^{6}) + 5 x (- 2)}{5 x y^{2}}$

Step 2.5

Factor $5 x$ out of $5 x (x^{3} y^{2} + 4 y^{6}) + 5 x (- 2)$ .

$\frac{5 x (x^{3} y^{2} + 4 y^{6} - 2)}{5 x y^{2}}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$\frac{5 x (x^{3} y^{2} + 4 y^{6} - 2)}{5 x y^{2}}$

Step 3.2

Rewrite the expression.

$\frac{x (x^{3} y^{2} + 4 y^{6} - 2)}{x y^{2}}$

Step 4

Cancel the common factor of $x$ .

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Step 4.1

Cancel the common factor.

$\frac{x (x^{3} y^{2} + 4 y^{6} - 2)}{x y^{2}}$

Step 4.2

Rewrite the expression.

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

Step 5

Split the fraction $\frac{x^{3} y^{2} + 4 y^{6} - 2}{y^{2}}$ into two fractions.

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

Step 6

Split the fraction $\frac{x^{3} y^{2} + 4 y^{6}}{y^{2}}$ into two fractions.

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

Step 7

Cancel the common factor of $y^{2}$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Divide $x^{3}$ by $1$ .

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

Step 8

Cancel the common factor of $y^{6}$ and $y^{2}$ .

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Step 8.1

Factor $y^{2}$ out of $4 y^{6}$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Multiply by $1$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

$x^{3} + \frac{4 y^{4}}{1} + \frac{- 2}{y^{2}}$

Step 8.2.4

Divide $4 y^{4}$ by $1$ .

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

Step 9

Move the negative in front of the fraction.

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