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

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

Evaluate

$$x\left(3x-2y\right)$$

Solution Steps

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

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

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

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

Calculate -x to the power of 2 and get x^{2}.

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

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

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

Combine 4x^{2} and -x^{2} to get 3x^{2}.

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

Multiply -2 and -1 to get 2.

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

Calculate -x to the power of 2 and get x^{2}.

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

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

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

Combine 4x^{2} and -x^{2} to get 3x^{2}.

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

Multiply -2 and -1 to get 2.

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

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

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

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

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