# How do you factor by grouping m^3 + 3m^2n + 3mn^2 +n^3?

May 14, 2015

${m}^{3} + {n}^{3} + 3 m n \left(m + n\right)$

= $\left(m + n\right) \left({m}^{2} - m n + {n}^{2}\right) + 3 m n \left(m + n\right)$

= $\left(m + n\right) \left({m}^{2} - m n + {n}^{2} + 3 m n\right)$

= $\left(m + n\right) \left({m}^{2} + 2 m n + {n}^{2}\right)$

= $\left(m + n\right) {\left(m + n\right)}^{2}$

= ${\left(m + n\right)}^{3}$