Factor 200m^4+80m^3+8m^2

$200 m^{4} + 80 m^{3} + 8 m^{2}$

Step 1

Factor $8 m^{2}$ out of $200 m^{4} + 80 m^{3} + 8 m^{2}$ .

Factor $8 m^{2}$ out of $200 m^{4}$ .

$8 m^{2} (25 m^{2}) + 80 m^{3} + 8 m^{2}$

Factor $8 m^{2}$ out of $80 m^{3}$ .

$8 m^{2} (25 m^{2}) + 8 m^{2} (10 m) + 8 m^{2}$

Factor $8 m^{2}$ out of $8 m^{2}$ .

$8 m^{2} (25 m^{2}) + 8 m^{2} (10 m) + 8 m^{2} (1)$

Factor $8 m^{2}$ out of $8 m^{2} (25 m^{2}) + 8 m^{2} (10 m)$ .

$8 m^{2} (25 m^{2} + 10 m) + 8 m^{2} (1)$

Factor $8 m^{2}$ out of $8 m^{2} (25 m^{2} + 10 m) + 8 m^{2} (1)$ .

$8 m^{2} (25 m^{2} + 10 m + 1)$

Step 2

Factor using the perfect square rule.

Rewrite $25 m^{2}$ as ${(5 m)}^{2}$ .

$8 m^{2} ({(5 m)}^{2} + 10 m + 1)$

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

$8 m^{2} ({(5 m)}^{2} + 10 m + 1^{2})$

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

$10 m = 2 \cdot (5 m) \cdot 1$

Rewrite the polynomial.

$8 m^{2} ({(5 m)}^{2} + 2 \cdot (5 m) \cdot 1 + 1^{2})$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 5 m$ and $b = 1$ .

$8 m^{2} {(5 m + 1)}^{2}$