Solve 4m^{4}p^{3}-4m^3p^4+4m^2p^2

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

Factor

$$4m^{2}p^{2}\left(1+pm^{2}-mp^{2}\right)$$

Solution Steps

Factor out 4.

$$4\left(m^{4}p^{3}-m^{3}p^{4}+m^{2}p^{2}\right)$$

Consider m^{4}p^{3}-m^{3}p^{4}+m^{2}p^{2}. Factor out m^{2}p^{2}.

$$m^{2}p^{2}\left(m^{2}p-mp^{2}+1\right)$$

Rewrite the complete factored expression.

$$4m^{2}p^{2}\left(m^{2}p-mp^{2}+1\right)$$

Evaluate

$$4\left(1+pm^{2}-mp^{2}\right)\left(mp\right)^{2}$$