Basic Math Examples

$u^{4} - 16 v^{4}$

Step 1

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

${(u^{2})}^{2} - 16 v^{4}$

Step 2

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

${(u^{2})}^{2} - {(4 v^{2})}^{2}$

Step 3

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

$(u^{2} + 4 v^{2}) (u^{2} - (4 v^{2}))$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Remove parentheses.

$(u^{2} + 4 v^{2}) (u^{2} - 1 \cdot 4 v^{2})$

Step 4.2

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

$(u^{2} + 4 v^{2}) (u^{2} - {(2 v)}^{2})$

Step 4.3

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

$(u^{2} + 4 v^{2}) ((u + 2 v) (u - (2 v)))$

Step 4.4

Factor.

Tap for more steps...

Step 4.4.1

Multiply $2$ by $- 1$ .

$(u^{2} + 4 v^{2}) ((u + 2 v) (u - 2 v))$

Step 4.4.2

Remove unnecessary parentheses.

$(u^{2} + 4 v^{2}) (u + 2 v) (u - 2 v)$