Solve x^{4}y+8x^3y-6x^2y^2-48xy^2

$$x ^ { 4 } y + 8 x ^ { 3 } y - 6 x ^ { 2 } y ^ { 2 } - 48 x y ^ { 2 }$$

Factor

$$xy\left(x+8\right)\left(x^{2}-6y\right)$$

Solution Steps

Factor out xy.

$$xy\left(x^{3}+8x^{2}-6xy-48y\right)$$

Consider x^{3}+8x^{2}-6xy-48y. Do the grouping x^{3}+8x^{2}-6xy-48y=\left(x^{3}+8x^{2}\right)+\left(-6xy-48y\right), and factor out x^{2} in the first and -6y in the second group.

$$x^{2}\left(x+8\right)-6y\left(x+8\right)$$

Factor out common term x+8 by using distributive property.

$$\left(x+8\right)\left(x^{2}-6y\right)$$

Rewrite the complete factored expression.

$$xy\left(x+8\right)\left(x^{2}-6y\right)$$

Evaluate

$$xy\left(x+8\right)\left(x^{2}-6y\right)$$