Factor 4mn^2-4m^2n^2+m^3n^2

$4 m n^{2} - 4 m^{2} n^{2} + m^{3} n^{2}$

Step 1

Factor $m n^{2}$ out of $4 m n^{2} - 4 m^{2} n^{2} + m^{3} n^{2}$ .

Factor $m n^{2}$ out of $4 m n^{2}$ .

$m n^{2} (4) - 4 m^{2} n^{2} + m^{3} n^{2}$

Factor $m n^{2}$ out of $- 4 m^{2} n^{2}$ .

$m n^{2} (4) + m n^{2} (- 4 m) + m^{3} n^{2}$

Factor $m n^{2}$ out of $m^{3} n^{2}$ .

$m n^{2} (4) + m n^{2} (- 4 m) + m n^{2} (m^{2})$

Factor $m n^{2}$ out of $m n^{2} (4) + m n^{2} (- 4 m)$ .

$m n^{2} (4 - 4 m) + m n^{2} (m^{2})$

Factor $m n^{2}$ out of $m n^{2} (4 - 4 m) + m n^{2} (m^{2})$ .

$m n^{2} (4 - 4 m + m^{2})$

Step 2

Factor using the perfect square rule.

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

$m n^{2} (2^{2} - 4 m + m^{2})$

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

$4 m = 2 \cdot 2 \cdot m$

Rewrite the polynomial.

$m n^{2} (2^{2} - 2 \cdot 2 \cdot m + m^{2})$

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

$m n^{2} {(2 - m)}^{2}$