Algebra Examples

$81 - 16 x^{4}$

Step 1

Rewrite $81$ as $9^{2}$ .

$9^{2} - 16 x^{4}$

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Remove parentheses.

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

Step 4.2

Rewrite $9$ as $3^{2}$ .

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

Step 4.3

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

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

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 $a = 3$ and $b = 2 x$ .

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

Step 4.5

Factor.

Tap for more steps...

Step 4.5.1

Multiply $2$ by $- 1$ .

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

Step 4.5.2

Remove unnecessary parentheses.

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