# How do you combine (5x^2 - 3x^2y + 2y^2x - y) - (2xy^2 - y - 5x^2 + 3yx^2)?

May 2, 2015

The answer is $10 {x}^{2} - 6 {x}^{2} y$ .

Combine:

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

Make the variables consistent. $3 {x}^{2} y = 3 y {x}^{2}$ and $2 {y}^{2} x = 2 x {y}^{2}$.

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

The minus sign in front of the second set of parentheses is like multiplying by $- 1$, and indicates that the sign of each of the terms inside the second set of parentheses will be reversed.

Remove the second set of parentheses and change the signs of the terms.

(5x^2-3x^2y+2xy^2-y)-2xy^2+y+5x^2-3x^2y)

Remove the first set of parentheses.

5x^2-3x^2y+2xy^2-y-2xy^2+y+5x^2-3x^2y)

Combine like terms.

$5 {x}^{2} + 5 {x}^{2} - 3 {x}^{2} y - 3 {x}^{2} y \cancel{+ 2 x {y}^{2}} \cancel{- 2 x {y}^{2}} \cancel{- y} \cancel{+ y}$=

$10 {x}^{2} - 6 {x}^{2} y$