Algebra Examples

x^{2} + 6 x + 9

$x^{2} + 6 x + 9$

Step 1

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

x^{2} + 6 x + 3^{2}

$x^{2} + 6 x + 3^{2}$

Step 2

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

6 x = 2 \cdot x \cdot 3

$6 x = 2 \cdot x \cdot 3$

Step 3

Rewrite the polynomial.

x^{2} + 2 \cdot x \cdot 3 + 3^{2}

$x^{2} + 2 \cdot x \cdot 3 + 3^{2}$

Step 4

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 = x

$a = x$ and

b = 3

$b = 3$ .

{(x + 3)}^{2}

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

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