Examples

x^{2} + 2 x + 1

$x^{2} + 2 x + 1$

Step 1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

x^{2} + 2 x + 1^{2}

$x^{2} + 2 x + 1^{2}$

Step 2

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

2 x = 2 \cdot x \cdot 1

$2 x = 2 \cdot x \cdot 1$

Step 3

Rewrite the polynomial.

x^{2} + 2 \cdot x \cdot 1 + 1^{2}

$x^{2} + 2 \cdot x \cdot 1 + 1^{2}$

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 = 1

$b = 1$ .

{(x + 1)}^{2}

${(x + 1)}^{2}$

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