# How do you simplify 7xy (x^2 + y) - 11 xy^2 (x^2 -1)?

Jul 16, 2015

$7 {x}^{3} y - 11 {x}^{3} {y}^{2} + 18 x {y}^{2} = x y \left(7 {x}^{2} y - 11 {x}^{2} y + 18 {y}^{2}\right)$

#### Explanation:

First, distribute the outer terms into the brackets:

$7 x y \left({x}^{2} + y\right) - 11 x {y}^{2} \left({x}^{2} - 1\right)$
=$\left(7 x y \cdot {x}^{2} + 7 x y \cdot y\right) + \left(- 11 x {y}^{2} \cdot {x}^{2} + 11 x {y}^{2}\right)$

Simplify using exponent rules

$= 7 {x}^{3} y + 7 x {y}^{2} - 11 {x}^{3} {y}^{2} + 11 x {y}^{2}$

$= 7 {x}^{3} y - 11 {x}^{3} {y}^{2} + 18 x {y}^{2}$
If you want, you can factor out an $x y$ to simplify further
$= x y \left(7 {x}^{2} y - 11 {x}^{2} y + 18 {y}^{2}\right)$