Algebra Examples

$\frac{9}{25} a^{2} - \frac{49}{36} b^{2}$

Step 1

Rewrite $\frac{9}{25} a^{2}$ as ${(\frac{3}{5} a)}^{2}$ .

${(\frac{3}{5} a)}^{2} - \frac{49}{36} b^{2}$

Step 2

Rewrite $\frac{49}{36} b^{2}$ as ${(\frac{7}{6} b)}^{2}$ .

${(\frac{3}{5} a)}^{2} - {(\frac{7}{6} b)}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{3}{5} a$ and $b = \frac{7}{6} b$ .

$(\frac{3}{5} a + \frac{7}{6} b) (\frac{3}{5} a - (\frac{7}{6} b))$

Step 4

Simplify.

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Step 4.1

Combine $\frac{3}{5}$ and $a$ .

$(\frac{3 a}{5} + \frac{7}{6} b) (\frac{3}{5} a - (\frac{7}{6} b))$

Step 4.2

Combine $\frac{7}{6}$ and $b$ .

$(\frac{3 a}{5} + \frac{7 b}{6}) (\frac{3}{5} a - (\frac{7}{6} b))$

Step 4.3

Combine $\frac{3}{5}$ and $a$ .

$(\frac{3 a}{5} + \frac{7 b}{6}) (\frac{3 a}{5} - (\frac{7}{6} b))$

Step 4.4

Combine $\frac{7}{6}$ and $b$ .

$(\frac{3 a}{5} + \frac{7 b}{6}) (\frac{3 a}{5} - \frac{7 b}{6})$