Solve 4(x-y)^2-(2x+y)(-y+2x)

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

Evaluate

$$y\left(5y-8x\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.

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

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

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

Use the distributive property to multiply 2x+y by -y+2x.

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

To find the opposite of 2x\left(-y\right)+4x^{2}+y\left(-y\right)+2yx, find the opposite of each term.

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

Multiply -2 and -1 to get 2.

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

Combine -8xy and 2xy to get -6xy.

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

Combine 4x^{2} and -4x^{2} to get 0.

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

Multiply -1 and -1 to get 1.

$$-6xy+4y^{2}+yy-2yx$$

Multiply y and y to get y^{2}.

$$-6xy+4y^{2}+y^{2}-2yx$$

Combine 4y^{2} and y^{2} to get 5y^{2}.

$$-6xy+5y^{2}-2yx$$

Combine -6xy and -2yx to get -8xy.

$$-8xy+5y^{2}$$

Expand

$$5y^{2}-8xy$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-y\right)^{2}.

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

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

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

Use the distributive property to multiply 2x+y by -y+2x.

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

To find the opposite of 2x\left(-y\right)+4x^{2}+y\left(-y\right)+2yx, find the opposite of each term.

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

Multiply -2 and -1 to get 2.

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

Combine -8xy and 2xy to get -6xy.

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

Combine 4x^{2} and -4x^{2} to get 0.

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

Multiply -1 and -1 to get 1.

$$-6xy+4y^{2}+yy-2yx$$

Multiply y and y to get y^{2}.

$$-6xy+4y^{2}+y^{2}-2yx$$

Combine 4y^{2} and y^{2} to get 5y^{2}.

$$-6xy+5y^{2}-2yx$$

Combine -6xy and -2yx to get -8xy.

$$-8xy+5y^{2}$$