Algebra Examples

x^{2} + 20 x + 100

$x^{2} + 20 x + 100$

Step 1

Rewrite

100

$100$ as

10^{2}

$10^{2}$ .

x^{2} + 20 x + 10^{2}

$x^{2} + 20 x + 10^{2}$

Step 2

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

20 x = 2 \cdot x \cdot 10

$20 x = 2 \cdot x \cdot 10$

Step 3

Rewrite the polynomial.

x^{2} + 2 \cdot x \cdot 10 + 10^{2}

$x^{2} + 2 \cdot x \cdot 10 + 10^{2}$

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 = 10

$b = 10$ .

{(x + 10)}^{2}

${(x + 10)}^{2}$