Solve p^{3}t^{3}+mn^{2}p^{2}t+m^2npt^2+m^3n^3

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

Factor

$$\left(mn^{2}+pt^{2}\right)\left(nm^{2}+tp^{2}\right)$$

Solution Steps

Do the grouping p^{3}t^{3}+mn^{2}p^{2}t+m^{2}npt^{2}+m^{3}n^{3}=\left(p^{3}t^{3}+mn^{2}p^{2}t\right)+\left(m^{2}npt^{2}+m^{3}n^{3}\right), and factor out tp^{2} in the first and nm^{2} in the second group.

$$tp^{2}\left(mn^{2}+pt^{2}\right)+nm^{2}\left(mn^{2}+pt^{2}\right)$$

Factor out common term mn^{2}+pt^{2} by using distributive property.

$$\left(mn^{2}+pt^{2}\right)\left(tp^{2}+nm^{2}\right)$$

Evaluate

$$\left(mn^{2}+pt^{2}\right)\left(nm^{2}+tp^{2}\right)$$