Calculus Examples

$x^{4} y - x y^{4}$

Step 1

Factor $x y$ out of $x^{4} y - x y^{4}$ .

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Step 1.1

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

$x y (x^{3}) - x y^{4}$

Step 1.2

Factor $x y$ out of $- x y^{4}$ .

$x y (x^{3}) + x y (- 1 y^{3})$

Step 1.3

Factor $x y$ out of $x y (x^{3}) + x y (- 1 y^{3})$ .

$x y (x^{3} - 1 y^{3})$

Step 2

Factor.

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Step 2.1

Since both terms are perfect cubes, factor using the difference of cubes formula, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ where $a = x$ and $b = y$ .

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

Step 2.2

Remove unnecessary parentheses.

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