Algebra Examples

81 x^{4} - 16

$81 x^{4} - 16$

Step 1

Rewrite

81 x^{4}

$81 x^{4}$ as

{(9 x^{2})}^{2}

${(9 x^{2})}^{2}$ .

{(9 x^{2})}^{2} - 16

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

Step 2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

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

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = 9 x^{2}

$a = 9 x^{2}$ and

b = 4

$b = 4$ .

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

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Rewrite

9 x^{2}

$9 x^{2}$ as

{(3 x)}^{2}

${(3 x)}^{2}$ .

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

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

Step 4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

Step 4.3

Factor.

Tap for more steps...

Step 4.3.1

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = 3 x

$a = 3 x$ and

b = 2

$b = 2$ .

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

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

Step 4.3.2

Remove unnecessary parentheses.

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

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

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

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

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

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