Basic Math Examples

$\frac{9}{4} z^{2} + 2 z y + \frac{4}{9} y^{2}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $\frac{9}{4} z^{2}$ as ${(\frac{3}{2} z)}^{2}$ .

${(\frac{3}{2} z)}^{2} + 2 z y + \frac{4}{9} y^{2}$

Step 1.2

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

${(\frac{3}{2} z)}^{2} + 2 z y + {(\frac{2}{3} y)}^{2}$

Step 1.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 z y = 2 \cdot (\frac{3}{2} z) \cdot (\frac{2}{3} y)$

Step 1.4

Rewrite the polynomial.

${(\frac{3}{2} z)}^{2} + 2 \cdot (\frac{3}{2} z) \cdot (\frac{2}{3} y) + {(\frac{2}{3} y)}^{2}$

Step 1.5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = \frac{3}{2} z$ and $b = \frac{2}{3} y$ .

${(\frac{3}{2} z + \frac{2}{3} y)}^{2}$

Step 2

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

${(\frac{3 z}{2} + \frac{2}{3} y)}^{2}$

Step 3

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

${(\frac{3 z}{2} + \frac{2 y}{3})}^{2}$