Solve (9x^{2}y+3x^{2}-4y^{2})+(-7x^{2}y-4x^2+3y^2)-(2x^2y+7y^2)

$$( 9 x ^ { 2 } y + 3 x ^ { 2 } - 4 y ^ { 2 } ) + ( - 7 x ^ { 2 } y - 4 x ^ { 2 } + 3 y ^ { 2 } ) - ( 2 x ^ { 2 } y + 7 y ^ { 2 } )$$

Evaluate

$$-x^{2}-8y^{2}$$

Solution Steps

Combine 9x^{2}y and -7x^{2}y to get 2x^{2}y.

$$2x^{2}y+3x^{2}-4y^{2}-4x^{2}+3y^{2}-\left(2x^{2}y+7y^{2}\right)$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$2x^{2}y-x^{2}-4y^{2}+3y^{2}-\left(2x^{2}y+7y^{2}\right)$$

Combine -4y^{2} and 3y^{2} to get -y^{2}.

$$2x^{2}y-x^{2}-y^{2}-\left(2x^{2}y+7y^{2}\right)$$

To find the opposite of 2x^{2}y+7y^{2}, find the opposite of each term.

$$2x^{2}y-x^{2}-y^{2}-2x^{2}y-7y^{2}$$

Combine 2x^{2}y and -2x^{2}y to get 0.

$$-x^{2}-y^{2}-7y^{2}$$

Combine -y^{2} and -7y^{2} to get -8y^{2}.

$$-x^{2}-8y^{2}$$

Expand

$$-x^{2}-8y^{2}$$

Solution Steps

Combine 9x^{2}y and -7x^{2}y to get 2x^{2}y.

$$2x^{2}y+3x^{2}-4y^{2}-4x^{2}+3y^{2}-\left(2x^{2}y+7y^{2}\right)$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$2x^{2}y-x^{2}-4y^{2}+3y^{2}-\left(2x^{2}y+7y^{2}\right)$$

Combine -4y^{2} and 3y^{2} to get -y^{2}.

$$2x^{2}y-x^{2}-y^{2}-\left(2x^{2}y+7y^{2}\right)$$

To find the opposite of 2x^{2}y+7y^{2}, find the opposite of each term.

$$2x^{2}y-x^{2}-y^{2}-2x^{2}y-7y^{2}$$

Combine 2x^{2}y and -2x^{2}y to get 0.

$$-x^{2}-y^{2}-7y^{2}$$

Combine -y^{2} and -7y^{2} to get -8y^{2}.

$$-x^{2}-8y^{2}$$