Precalculus Examples

$\frac{4}{25} y^{2} - 64$

Step 1

Rewrite $\frac{4}{25} y^{2}$ as ${(\frac{2}{5} y)}^{2}$ .

${(\frac{2}{5} y)}^{2} - 64$

Step 2

Rewrite $64$ as $8^{2}$ .

${(\frac{2}{5} y)}^{2} - 8^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{2}{5} y$ and $b = 8$ .

$(\frac{2}{5} y + 8) (\frac{2}{5} y - 8)$

Step 4

Simplify.

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Step 4.1

Combine $\frac{2}{5}$ and $y$ .

$(\frac{2 y}{5} + 8) (\frac{2}{5} y - 8)$

Step 4.2

Factor $2$ out of $\frac{2 y}{5} + 8$ .

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Step 4.2.1

Factor $2$ out of $\frac{2 y}{5}$ .

$(2 \frac{y}{5} + 8) (\frac{2}{5} y - 8)$

Step 4.2.2

Factor $2$ out of $8$ .

$(2 \frac{y}{5} + 2 \cdot 4) (\frac{2}{5} y - 8)$

Step 4.2.3

Factor $2$ out of $2 \frac{y}{5} + 2 \cdot 4$ .

$2 (\frac{y}{5} + 4) (\frac{2}{5} y - 8)$

Step 4.3

Combine $\frac{2}{5}$ and $y$ .

$2 (\frac{y}{5} + 4) (\frac{2 y}{5} - 8)$

Step 5

Factor.

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Step 5.1

Factor $2$ out of $\frac{2 y}{5} - 8$ .

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Step 5.1.1

Factor $2$ out of $\frac{2 y}{5}$ .

$2 (\frac{y}{5} + 4) (2 \frac{y}{5} - 8)$

Step 5.1.2

Factor $2$ out of $- 8$ .

$2 (\frac{y}{5} + 4) (2 \frac{y}{5} + 2 \cdot - 4)$

Step 5.1.3

Factor $2$ out of $2 \frac{y}{5} + 2 \cdot - 4$ .

$2 (\frac{y}{5} + 4) (2 (\frac{y}{5} - 4))$

Step 5.2

Remove unnecessary parentheses.

$2 (\frac{y}{5} + 4) \cdot 2 (\frac{y}{5} - 4)$

Step 6

Multiply $2$ by $2$ .

$4 (\frac{y}{5} + 4) (\frac{y}{5} - 4)$