Algebra Examples

$81 x^{4} - 16 y^{4}$

Step 1

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

${(9 x^{2})}^{2} - 16 y^{4}$

Step 2

Rewrite $16 y^{4}$ as ${(4 y^{2})}^{2}$ .

${(9 x^{2})}^{2} - {(4 y^{2})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 9 x^{2}$ and $b = 4 y^{2}$ .

$(9 x^{2} + 4 y^{2}) (9 x^{2} - (4 y^{2}))$

Step 4

Simplify.

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Step 4.1

Remove parentheses.

$(9 x^{2} + 4 y^{2}) (9 x^{2} - 1 \cdot 4 y^{2})$

Step 4.2

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

$(9 x^{2} + 4 y^{2}) ({(3 x)}^{2} - 1 \cdot 4 y^{2})$

Step 4.3

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

$(9 x^{2} + 4 y^{2}) ({(3 x)}^{2} - {(2 y)}^{2})$

Step 4.4

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

$(9 x^{2} + 4 y^{2}) ((3 x + 2 y) (3 x - (2 y)))$

Step 4.5

Factor.

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Step 4.5.1

Multiply $2$ by $- 1$ .

$(9 x^{2} + 4 y^{2}) ((3 x + 2 y) (3 x - 2 y))$

Step 4.5.2

Remove unnecessary parentheses.

$(9 x^{2} + 4 y^{2}) (3 x + 2 y) (3 x - 2 y)$