Solve 4xy-[2(x^2+xy-2y^2)-3(x^2-2xy+y2)]

$$4 x y - [ 2 ( x ^ { 2 } + x y - 2 y ^ { 2 } ) - 3 ( x ^ { 2 } - 2 x y + y 2 ) ]$$

Evaluate

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

Solution Steps

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

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

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

$$4xy-\left(2x^{2}+2xy-4y^{2}-3x^{2}+6xy-3y_{2}\right)$$

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

$$4xy-\left(-x^{2}+2xy-4y^{2}+6xy-3y_{2}\right)$$

Combine 2xy and 6xy to get 8xy.

$$4xy-\left(-x^{2}+8xy-4y^{2}-3y_{2}\right)$$

To find the opposite of -x^{2}+8xy-4y^{2}-3y_{2}, find the opposite of each term.

$$4xy+x^{2}-8xy+4y^{2}+3y_{2}$$

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

$$-4xy+x^{2}+4y^{2}+3y_{2}$$

Expand

$$x^{2}-4xy+4y^{2}+3y_{2}$$

Solution Steps

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

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

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

$$4xy-\left(2x^{2}+2xy-4y^{2}-3x^{2}+6xy-3y_{2}\right)$$

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

$$4xy-\left(-x^{2}+2xy-4y^{2}+6xy-3y_{2}\right)$$

Combine 2xy and 6xy to get 8xy.

$$4xy-\left(-x^{2}+8xy-4y^{2}-3y_{2}\right)$$

To find the opposite of -x^{2}+8xy-4y^{2}-3y_{2}, find the opposite of each term.

$$4xy+x^{2}-8xy+4y^{2}+3y_{2}$$

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

$$-4xy+x^{2}+4y^{2}+3y_{2}$$