Algebra Examples

$4 x^{2} + 2 x + \frac{1}{4}$

Step 1

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

${(2 x)}^{2} + 2 x + \frac{1}{4}$

Step 2

Rewrite $1$ as $1^{2}$ .

${(2 x)}^{2} + 2 x + \frac{1^{2}}{4}$

Step 3

Rewrite $4$ as $2^{2}$ .

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

Step 4

Rewrite $\frac{1^{2}}{2^{2}}$ as ${(\frac{1}{2})}^{2}$ .

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

Step 5

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

$2 x = 2 \cdot (2 x) \cdot \frac{1}{2}$

Step 6

Rewrite the polynomial.

${(2 x)}^{2} + 2 \cdot (2 x) \cdot \frac{1}{2} + {(\frac{1}{2})}^{2}$

Step 7

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 2 x$ and $b = \frac{1}{2}$ .

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