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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply 3 by x+y.

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

Use the distributive property to multiply 3x+3y by x-y and combine like terms.

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

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

Use the distributive property to multiply 3 by x+y.

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

Use the distributive property to multiply 3x+3y by x-y and combine like terms.

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

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

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

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

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

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

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

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

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