Factor m^2+m+1/4

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

Step 1

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

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

Step 2

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

$m^{2} + m + \frac{1^{2}}{2^{2}}$

Step 3

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

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

Step 4

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

$m = 2 \cdot m \cdot \frac{1}{2}$

Step 5

Rewrite the polynomial.

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

Step 6

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

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