Solve 24x^3z+24xy^2z-16x^2yz-16y^3z

$$24 x ^ { 3 } z + 24 x y ^ { 2 } z - 16 x ^ { 2 } y z - 16 y ^ { 3 } z$$

Factor

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

Solution Steps

Factor out 8.

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

Consider 3x^{3}z+3xy^{2}z-2x^{2}yz-2y^{3}z. Factor out z.

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

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

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

Factor out common term x^{2}+y^{2} by using distributive property.

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

Rewrite the complete factored expression.

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

Evaluate

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