Algebra Examples

$x^{6} y^{4} (x^{4} - 16) - 9 (x^{4} - 16)$

Step 1

Factor $x^{4} - 16$ out of $x^{6} y^{4} (x^{4} - 16) - 9 (x^{4} - 16)$ .

Tap for more steps...

Step 1.1

Factor $x^{4} - 16$ out of $x^{6} y^{4} (x^{4} - 16)$ .

$(x^{4} - 16) (x^{6} y^{4}) - 9 (x^{4} - 16)$

Step 1.2

Factor $x^{4} - 16$ out of $- 9 (x^{4} - 16)$ .

$(x^{4} - 16) (x^{6} y^{4}) + (x^{4} - 16) \cdot - 9$

Step 1.3

Factor $x^{4} - 16$ out of $(x^{4} - 16) (x^{6} y^{4}) + (x^{4} - 16) \cdot - 9$ .

$(x^{4} - 16) (x^{6} y^{4} - 9)$

Step 2

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

$({(x^{2})}^{2} - 16) (x^{6} y^{4} - 9)$

Step 3

Rewrite $16$ as $4^{2}$ .

$({(x^{2})}^{2} - 4^{2}) (x^{6} y^{4} - 9)$

Step 4

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 $b = 4$ .

$(x^{2} + 4) (x^{2} - 4) (x^{6} y^{4} - 9)$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Rewrite $4$ as $2^{2}$ .

$(x^{2} + 4) (x^{2} - 2^{2}) (x^{6} y^{4} - 9)$

Step 5.2

Factor.

Tap for more steps...

Step 5.2.1

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 $b = 2$ .

$(x^{2} + 4) ((x + 2) (x - 2)) (x^{6} y^{4} - 9)$

Step 5.2.2

Remove unnecessary parentheses.

$(x^{2} + 4) (x + 2) (x - 2) (x^{6} y^{4} - 9)$

Step 6

Rewrite $x^{6} y^{4}$ as ${(x^{3} y^{2})}^{2}$ .

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

Step 7

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

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

Step 8

Factor.

Tap for more steps...

Step 8.1

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

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

Step 8.2

Remove unnecessary parentheses.

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