Factor m^2+2mn+n^2

$m^{2} + 2 m n + n^{2}$

Step 1

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

$2 m n = 2 \cdot m \cdot n$

Step 2

Rewrite the polynomial.

$m^{2} + 2 \cdot m \cdot n + n^{2}$

Step 3

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

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