Pre-Algebra Examples

$x^{3} + x^{2} - y^{3} - y^{2}$

Step 1

Regroup terms.

$x^{3} - y^{3} + x^{2} - y^{2}$

Step 2

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 $b = y$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

Factor $x - y$ out of $(x + y) (x - y)$ .

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

Step 4.2

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

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