Algebra Examples

$x^{4} - 81 y^{4}$

Step 1

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

${(x^{2})}^{2} - 81 y^{4}$

Step 2

Rewrite $81 y^{4}$ as ${(9 y^{2})}^{2}$ .

${(x^{2})}^{2} - {(9 y^{2})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = 9 y^{2}$ .

$(x^{2} + 9 y^{2}) (x^{2} - (9 y^{2}))$

Step 4

Simplify.

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Step 4.1

Remove parentheses.

$(x^{2} + 9 y^{2}) (x^{2} - 1 \cdot 9 y^{2})$

Step 4.2

Rewrite $9 y^{2}$ as ${(3 y)}^{2}$ .

$(x^{2} + 9 y^{2}) (x^{2} - {(3 y)}^{2})$

Step 4.3

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 $b = 3 y$ .

$(x^{2} + 9 y^{2}) ((x + 3 y) (x - (3 y)))$

Step 4.4

Factor.

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Step 4.4.1

Multiply $3$ by $- 1$ .

$(x^{2} + 9 y^{2}) ((x + 3 y) (x - 3 y))$

Step 4.4.2

Remove unnecessary parentheses.

$(x^{2} + 9 y^{2}) (x + 3 y) (x - 3 y)$