Solve (-y^2+15y-22)-(2y^2+6y+10)+(5y^2+4y+19)

$$( - y ^ { 2 } + 15 y - 22 ) - ( 2 y ^ { 2 } + 6 y + 10 ) + ( 5 y ^ { 2 } + 4 y + 19 )$$

Evaluate

$$2y^{2}+13y-13$$

Solution Steps

To find the opposite of 2y^{2}+6y+10, find the opposite of each term.

$$-y^{2}+15y-22-2y^{2}-6y-10+5y^{2}+4y+19$$

Combine 15y and -6y to get 9y.

$$-y^{2}+9y-22-2y^{2}-10+5y^{2}+4y+19$$

Subtract 10 from -22 to get -32.

$$-y^{2}+9y-32-2y^{2}+5y^{2}+4y+19$$

Combine -2y^{2} and 5y^{2} to get 3y^{2}.

$$-y^{2}+9y-32+3y^{2}+4y+19$$

Combine 9y and 4y to get 13y.

$$-y^{2}+13y-32+3y^{2}+19$$

Add -32 and 19 to get -13.

$$-y^{2}+13y-13+3y^{2}$$

Combine -y^{2} and 3y^{2} to get 2y^{2}.

$$2y^{2}+13y-13$$

Expand

$$2y^{2}+13y-13$$

Solution Steps

To find the opposite of 2y^{2}+6y+10, find the opposite of each term.

$$-y^{2}+15y-22-2y^{2}-6y-10+5y^{2}+4y+19$$

Combine 15y and -6y to get 9y.

$$-y^{2}+9y-22-2y^{2}-10+5y^{2}+4y+19$$

Subtract 10 from -22 to get -32.

$$-y^{2}+9y-32-2y^{2}+5y^{2}+4y+19$$

Combine -2y^{2} and 5y^{2} to get 3y^{2}.

$$-y^{2}+9y-32+3y^{2}+4y+19$$

Combine 9y and 4y to get 13y.

$$-y^{2}+13y-32+3y^{2}+19$$

Add -32 and 19 to get -13.

$$-y^{2}+13y-13+3y^{2}$$

Combine -y^{2} and 3y^{2} to get 2y^{2}.

$$2y^{2}+13y-13$$