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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

Combine 2xy and 4xy to get 6xy.

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

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

$$-3x^{2}+6xy$$

Expand

$$6xy-3x^{2}$$

Solution Steps

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

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

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

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

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

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

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

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

Combine 2xy and 4xy to get 6xy.

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

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

$$-3x^{2}+6xy$$