Algebra Examples

$\frac{3}{2} a^{2} - 2 a b + \frac{2}{3} b^{2}$

Step 1

Factor $\frac{1}{6}$ out of each term.

$\frac{1}{6} (9 a^{2} - 12 a b + 4 b^{2})$

Step 2

Factor using the perfect square rule.

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Step 2.1

Rewrite $9 a^{2}$ as ${(3 a)}^{2}$ .

$\frac{1}{6} \cdot ({(3 a)}^{2} - 12 a b + 4 b^{2})$

Step 2.2

Rewrite $4 b^{2}$ as ${(2 b)}^{2}$ .

$\frac{1}{6} \cdot ({(3 a)}^{2} - 12 a b + {(2 b)}^{2})$

Step 2.3

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

$12 a b = 2 \cdot (3 a) \cdot (2 b)$

Step 2.4

Rewrite the polynomial.

$\frac{1}{6} \cdot ({(3 a)}^{2} - 2 \cdot (3 a) \cdot (2 b) + {(2 b)}^{2})$

Step 2.5

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

$\frac{1}{6} \cdot {(3 a - 2 b)}^{2}$