Algebra Examples

$4 x^{2} + 20 x + 25$

Step 1

Rewrite

$4 x^{2}$ as

${(2 x)}^{2}$ .

${(2 x)}^{2} + 20 x + 25$

Step 2

Rewrite

$25$ as

$5^{2}$ .

${(2 x)}^{2} + 20 x + 5^{2}$

Step 3

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

$20 x = 2 \cdot (2 x) \cdot 5$

Step 4

Rewrite the polynomial.

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

Step 5

Factor using the perfect square trinomial rule

$a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where

$a = 2 x$ and

$b = 5$ .

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