# How do you simplify -x^2z(2z^2+4xz^3)+xz^2(xz+5x^3z)+x^2z^3(3x^2z+4xz)?

May 3, 2018

$8 {x}^{4} {z}^{3} - {x}^{2} {z}^{3}$

#### Explanation:

Expand each bracket and then collect like terms

$- {x}^{2} z \left(2 {z}^{2} + 4 x {z}^{3}\right) + x {z}^{2} \left(x z + 5 {x}^{3} z\right) + {x}^{2} {z}^{3} \left(3 {x}^{2} z + 4 x z\right)$

$- 2 {x}^{2} {z}^{3} - 4 {x}^{3} {z}^{4} + {x}^{2} {z}^{3} + 5 {x}^{4} {z}^{3} + 3 {x}^{4} {z}^{3} + 4 {x}^{3} {z}^{4}$

$8 {x}^{4} {z}^{3} - {x}^{2} {z}^{3}$