Solve m^3+3m^2n+3mm^2+n^3

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

Factor

$$\left(m+n\right)\left(4m^{2}-mn+n^{2}\right)$$

Solution Steps

Multiply and combine like terms.

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

Consider 4m^{3}+n^{3}+3nm^{2} as a polynomial over variable m.

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

Find one factor of the form km^{p}+q, where km^{p} divides the monomial with the highest power 4m^{3} and q divides the constant factor n^{3}. One such factor is m+n. Factor the polynomial by dividing it by this factor.

$$\left(m+n\right)\left(4m^{2}-mn+n^{2}\right)$$

Evaluate

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