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

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

Step 1

Remove parentheses.

$3 x^{2} + 2 y^{2} - 5 x + y + 2 x^{2} - 2 x y - 2 y^{2} - 5 x + 3 y$

Step 2

Combine the opposite terms in $3 x^{2} + 2 y^{2} - 5 x + y + 2 x^{2} - 2 x y - 2 y^{2} - 5 x + 3 y$ .

Subtract $2 y^{2}$ from $2 y^{2}$ .

$3 x^{2} - 5 x + y + 2 x^{2} - 2 x y + 0 - 5 x + 3 y$

Add $3 x^{2} - 5 x + y + 2 x^{2} - 2 x y$ and $0$ .

$3 x^{2} - 5 x + y + 2 x^{2} - 2 x y - 5 x + 3 y$

Step 3

Add $3 x^{2}$ and $2 x^{2}$ .

$5 x^{2} - 5 x + y - 2 x y - 5 x + 3 y$

Step 4

Subtract $5 x$ from $- 5 x$ .

$5 x^{2} - 10 x + y - 2 x y + 3 y$

Step 5

Add $y$ and $3 y$ .

$5 x^{2} - 10 x - 2 x y + 4 y$

Step 6

Simplify the expression.

Move $- 10 x$ .

$5 x^{2} - 2 x y + 4 y - 10 x$

Reorder $5 x^{2}$ and $- 2 x y$ .

$- 2 x y + 5 x^{2} + 4 y - 10 x$