Algebra Examples

$x^{4} - y^{4} + x^{2} - y^{2}$

Step 1

Regroup terms.

$x^{4} - y^{4} + x^{2} - y^{2}$

Step 2

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

Step 3

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

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

Step 4

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

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

Step 5

Factor.

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Step 5.1

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 $b = y$ .

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

Step 5.2

Remove unnecessary parentheses.

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

Step 6

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 $b = y$ .

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

Step 7

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

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Step 7.1

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

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

Step 7.2

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

$(x + y) (x - y) (x^{2} + y^{2}) + (x + y) (x - y) (1)$

Step 7.3

Factor $(x + y) (x - y)$ out of $(x + y) (x - y) (x^{2} + y^{2}) + (x + y) (x - y) (1)$ .

$(x + y) (x - y) (x^{2} + y^{2} + 1)$