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

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

Evaluate

$$2\left(x-y\right)\left(2+y-x\right)$$

Solution Steps

Use the distributive property to multiply 4 by x-y.

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

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

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

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

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

Expand

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

Solution Steps

Use the distributive property to multiply 4 by x-y.

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

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

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

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

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