Algebra Examples

9 x^{2} - 12 x + 4

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

Step 1

Rewrite

9 x^{2}

$9 x^{2}$ as

{(3 x)}^{2}

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

{(3 x)}^{2} - 12 x + 4

${(3 x)}^{2} - 12 x + 4$

Step 2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

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 (3 x) \cdot 2

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

Step 4

Rewrite the polynomial.

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

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

Step 5

Factor using the perfect square trinomial rule

a^{2} - 2 a b + b^{2} = {(a - b)}^{2}

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

a = 3 x

$a = 3 x$ and

b = 2

$b = 2$ .

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

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