Algebra Examples

$1 - 81 x^{4}$

Step 1

Rewrite $1$ as $1^{2}$ .

$1^{2} - 81 x^{4}$

Step 2

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

$1^{2} - {(9 x^{2})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = 9 x^{2}$ .

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Remove parentheses.

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

Step 4.2

Rewrite $1$ as $1^{2}$ .

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

Step 4.3

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

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

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 $a = 1$ and $b = 3 x$ .

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

Step 4.5

Factor.

Tap for more steps...

Step 4.5.1

Multiply $3$ by $- 1$ .

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

Step 4.5.2

Remove unnecessary parentheses.

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