Factor 49m^4+140m^2+100

$49 m^{4} + 140 m^{2} + 100$

Step 1

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

$49 {(m^{2})}^{2} + 140 m^{2} + 100$

Step 2

Let $u = m^{2}$ . Substitute $u$ for all occurrences of $m^{2}$ .

$49 u^{2} + 140 u + 100$

Step 3

Factor using the perfect square rule.

Rewrite $49 u^{2}$ as ${(7 u)}^{2}$ .

${(7 u)}^{2} + 140 u + 100$

Rewrite $100$ as $10^{2}$ .

${(7 u)}^{2} + 140 u + 10^{2}$

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

$140 u = 2 \cdot (7 u) \cdot 10$

Rewrite the polynomial.

${(7 u)}^{2} + 2 \cdot (7 u) \cdot 10 + 10^{2}$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 7 u$ and $b = 10$ .

${(7 u + 10)}^{2}$

Step 4

Replace all occurrences of $u$ with $m^{2}$ .

${(7 m^{2} + 10)}^{2}$