Solve x^{3}y+x^{4}y^{2}+x^3y^2+x^4y^3=

$$x ^ { 3 } y + x ^ { 4 } y ^ { 2 } + x ^ { 3 } y ^ { 2 } + x ^ { 4 } y ^ { 3 } =$$

Factor

$$y\left(y+1\right)x^{3}\left(xy+1\right)$$

Solution Steps

Factor out x^{3}y.

$$x^{3}y\left(1+xy+y+xy^{2}\right)$$

Consider 1+xy+y+xy^{2}. Do the grouping 1+xy+y+xy^{2}=\left(1+xy\right)+\left(y+xy^{2}\right), and factor out y in y+xy^{2}.

$$xy+1+y\left(xy+1\right)$$

Factor out common term xy+1 by using distributive property.

$$\left(xy+1\right)\left(1+y\right)$$

Rewrite the complete factored expression.

$$x^{3}y\left(y+1\right)\left(xy+1\right)$$

Evaluate

$$y\left(y+1\right)x^{3}\left(xy+1\right)$$