Solve (5x^2+8xy+y^2)-(-x^2+4xy-5y^2

$$( 5 x ^ { 2 } + 8 x y + y ^ { 2 } ) - ( - x ^ { 2 } + 4 x y - 5 y ^ { 2 }$$

Evaluate

$$6x^{2}+4xy+6y^{2}$$

Solution Steps

To find the opposite of -x^{2}+4xy-5y^{2}, find the opposite of each term.

$$5x^{2}+8xy+y^{2}-\left(-x^{2}\right)-4xy+5y^{2}$$

Combine 8xy and -4xy to get 4xy.

$$5x^{2}+4xy+y^{2}-\left(-x^{2}\right)+5y^{2}$$

Combine y^{2} and 5y^{2} to get 6y^{2}.

$$5x^{2}+4xy+6y^{2}-\left(-x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$5x^{2}+4xy+6y^{2}+x^{2}$$

Combine 5x^{2} and x^{2} to get 6x^{2}.

$$6x^{2}+4xy+6y^{2}$$

Expand

$$6x^{2}+4xy+6y^{2}$$

Solution Steps

To find the opposite of -x^{2}+4xy-5y^{2}, find the opposite of each term.

$$5x^{2}+8xy+y^{2}-\left(-x^{2}\right)-4xy+5y^{2}$$

Combine 8xy and -4xy to get 4xy.

$$5x^{2}+4xy+y^{2}-\left(-x^{2}\right)+5y^{2}$$

Combine y^{2} and 5y^{2} to get 6y^{2}.

$$5x^{2}+4xy+6y^{2}-\left(-x^{2}\right)$$

Multiply -1 and -1 to get 1.

$$5x^{2}+4xy+6y^{2}+x^{2}$$

Combine 5x^{2} and x^{2} to get 6x^{2}.

$$6x^{2}+4xy+6y^{2}$$