Precalculus Examples

x^{2} + 12 x + 36

$x^{2} + 12 x + 36$

Step 1

Rewrite

36

$36$ as

6^{2}

$6^{2}$ .

x^{2} + 12 x + 6^{2}

$x^{2} + 12 x + 6^{2}$

Step 2

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

12 x = 2 \cdot x \cdot 6

$12 x = 2 \cdot x \cdot 6$

Step 3

Rewrite the polynomial.

x^{2} + 2 \cdot x \cdot 6 + 6^{2}

$x^{2} + 2 \cdot x \cdot 6 + 6^{2}$

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 = 6

$b = 6$ .

{(x + 6)}^{2}

${(x + 6)}^{2}$

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