Algebra Examples

x^{2} + 10 x + 25

$x^{2} + 10 x + 25$

Step 1

Rewrite

25

$25$ as

5^{2}

$5^{2}$ .

x^{2} + 10 x + 5^{2}

$x^{2} + 10 x + 5^{2}$

Step 2

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

10 x = 2 \cdot x \cdot 5

$10 x = 2 \cdot x \cdot 5$

Step 3

Rewrite the polynomial.

x^{2} + 2 \cdot x \cdot 5 + 5^{2}

$x^{2} + 2 \cdot x \cdot 5 + 5^{2}$

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 = 5

$b = 5$ .

{(x + 5)}^{2}

${(x + 5)}^{2}$

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