Basic Math Examples

$16 s^{4} - t^{4}$

Step 1

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

${(4 s^{2})}^{2} - t^{4}$

Step 2

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

${(4 s^{2})}^{2} - {(t^{2})}^{2}$

Step 3

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

$(4 s^{2} + t^{2}) (4 s^{2} - t^{2})$

Step 4

Simplify.

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Step 4.1

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

$(4 s^{2} + t^{2}) ({(2 s)}^{2} - t^{2})$

Step 4.2

Factor.

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Step 4.2.1

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

$(4 s^{2} + t^{2}) ((2 s + t) (2 s - t))$

Step 4.2.2

Remove unnecessary parentheses.

$(4 s^{2} + t^{2}) (2 s + t) (2 s - t)$