Factor 36+12m^2+m^4

$36 + 12 m^{2} + m^{4}$

Step 1

Rewrite $36$ as $6^{2}$ .

$6^{2} + 12 m^{2} + m^{4}$

Step 2

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

$6^{2} + 12 m^{2} + {(m^{2})}^{2}$

Step 3

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

$12 m^{2} = 2 \cdot 6 \cdot m^{2}$

Step 4

Rewrite the polynomial.

$6^{2} + 2 \cdot 6 \cdot m^{2} + {(m^{2})}^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 6$ and $b = m^{2}$ .

${(6 + m^{2})}^{2}$