Basic Math Examples

$16 z^{4} - 81$

Step 1

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

${(4 z^{2})}^{2} - 81$

Step 2

Rewrite $81$ as $9^{2}$ .

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 z^{2}$ and $b = 9$ .

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

Step 4

Simplify.

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

Factor.

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Step 4.3.1

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

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

Step 4.3.2

Remove unnecessary parentheses.

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