Algebra Examples

$x^{2} - \frac{2}{3} x + \frac{1}{9}$

Step 1

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

$x^{2} - \frac{x \cdot 2}{3} + \frac{1}{9}$

Step 2

Move $2$ to the left of $x$ .

$x^{2} - \frac{2 \cdot x}{3} + \frac{1}{9}$

Step 3

Multiply $2$ by $x$ .

$x^{2} - \frac{2 x}{3} + \frac{1}{9}$

Step 4

Factor using the perfect square rule.

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Step 4.1

Rewrite $1$ as $1^{2}$ .

$x^{2} - \frac{2 x}{3} + \frac{1^{2}}{9}$

Step 4.2

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

$x^{2} - \frac{2 x}{3} + \frac{1^{2}}{3^{2}}$

Step 4.3

Rewrite $\frac{1^{2}}{3^{2}}$ as ${(\frac{1}{3})}^{2}$ .

$x^{2} - \frac{2 x}{3} + {(\frac{1}{3})}^{2}$

Step 4.4

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

$\frac{2 x}{3} = 2 \cdot x \cdot \frac{1}{3}$

Step 4.5

Rewrite the polynomial.

$x^{2} - 2 \cdot x \cdot \frac{1}{3} + {(\frac{1}{3})}^{2}$

Step 4.6

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = \frac{1}{3}$ .

${(x - \frac{1}{3})}^{2}$