Algebra Examples

$\frac{4}{9} \cdot (x^{2} y^{2}) - \frac{25}{36} z^{2}$

Step 1

Remove parentheses.

$\frac{4}{9} \cdot x^{2} y^{2} - \frac{25}{36} z^{2}$

Step 2

Rewrite $\frac{4}{9} \cdot x^{2} y^{2}$ as ${(\frac{2}{3} x y)}^{2}$ .

${(\frac{2}{3} x y)}^{2} - \frac{25}{36} z^{2}$

Step 3

Rewrite $\frac{25}{36} z^{2}$ as ${(\frac{5}{6} z)}^{2}$ .

${(\frac{2}{3} x y)}^{2} - {(\frac{5}{6} z)}^{2}$

Step 4

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

$(\frac{2}{3} x y + \frac{5}{6} z) (\frac{2}{3} x y - (\frac{5}{6} z))$

Step 5

Simplify.

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Step 5.1

Combine $\frac{2}{3}$ and $x$ .

$(\frac{2 x}{3} y + \frac{5}{6} z) (\frac{2}{3} x y - (\frac{5}{6} z))$

Step 5.2

Combine $\frac{2 x}{3}$ and $y$ .

$(\frac{2 x y}{3} + \frac{5}{6} z) (\frac{2}{3} x y - (\frac{5}{6} z))$

Step 5.3

Combine $\frac{5}{6}$ and $z$ .

$(\frac{2 x y}{3} + \frac{5 z}{6}) (\frac{2}{3} x y - (\frac{5}{6} z))$

Step 5.4

Combine $\frac{2}{3}$ and $x$ .

$(\frac{2 x y}{3} + \frac{5 z}{6}) (\frac{2 x}{3} y - (\frac{5}{6} z))$

Step 5.5

Combine $\frac{2 x}{3}$ and $y$ .

$(\frac{2 x y}{3} + \frac{5 z}{6}) (\frac{2 x y}{3} - (\frac{5}{6} z))$

Step 5.6

Combine $\frac{5}{6}$ and $z$ .

$(\frac{2 x y}{3} + \frac{5 z}{6}) (\frac{2 x y}{3} - \frac{5 z}{6})$