Algebra Examples

$4 x^{2} - 12 x + 9$

Step 1

Rewrite

$4 x^{2}$ as

${(2 x)}^{2}$ .

${(2 x)}^{2} - 12 x + 9$

Step 2

Rewrite

$9$ as

$3^{2}$ .

${(2 x)}^{2} - 12 x + 3^{2}$

Step 3

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

$12 x = 2 \cdot (2 x) \cdot 3$

Step 4

Rewrite the polynomial.

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

Step 5

Factor using the perfect square trinomial rule

$a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where

$a = 2 x$ and

$b = 3$ .

${(2 x - 3)}^{2}$