Solve 2(3x^2+4xy-5y^2+2)-3(2x^2+xy-3y^2)-(5xy-{y}^2+1)

$$2(3 { x }^{ 2 } +4xy-5 { y }^{ 2 } +2)-3(2 { x }^{ 2 } +xy-3 { y }^{ 2 } )-(5xy- { y }^{ 2 } +1)$$

Evaluate

$$3$$

Solution Steps

Use the distributive property to multiply 2 by 3x^{2}+4xy-5y^{2}+2.

$$6x^{2}+8xy-10y^{2}+4-3\left(2x^{2}+xy-3y^{2}\right)-\left(5xy-y^{2}+1\right)$$

Use the distributive property to multiply -3 by 2x^{2}+xy-3y^{2}.

$$6x^{2}+8xy-10y^{2}+4-6x^{2}-3xy+9y^{2}-\left(5xy-y^{2}+1\right)$$

Combine 6x^{2} and -6x^{2} to get 0.

$$8xy-10y^{2}+4-3xy+9y^{2}-\left(5xy-y^{2}+1\right)$$

Combine 8xy and -3xy to get 5xy.

$$5xy-10y^{2}+4+9y^{2}-\left(5xy-y^{2}+1\right)$$

Combine -10y^{2} and 9y^{2} to get -y^{2}.

$$5xy-y^{2}+4-\left(5xy-y^{2}+1\right)$$

To find the opposite of 5xy-y^{2}+1, find the opposite of each term.

$$5xy-y^{2}+4-5xy+y^{2}-1$$

Combine 5xy and -5xy to get 0.

$$-y^{2}+4+y^{2}-1$$

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

$$4-1$$

Subtract 1 from 4 to get 3.

$$3$$

Factor

$$3$$