Solve 2(x-y)^2-3(y-x)^2

$$2 ( x - y ) ^ { 2 } - 3 ( y - x ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

$$2x^{2}-4xy+2y^{2}-3y^{2}+6yx-3x^{2}$$

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

$$2x^{2}-4xy-y^{2}+6yx-3x^{2}$$

Combine -4xy and 6yx to get 2xy.

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

$$2x^{2}-4xy+2y^{2}-3y^{2}+6yx-3x^{2}$$

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

$$2x^{2}-4xy-y^{2}+6yx-3x^{2}$$

Combine -4xy and 6yx to get 2xy.

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

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

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