Solve 9(x-y)^2-(x+y)^2

$$9 ( x - y ) ^ { 2 } - ( x + y ) ^ { 2 }$$

Evaluate

$$4\left(x-2y\right)\left(2x-y\right)$$

Solution Steps

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

$$9\left(x^{2}-2xy+y^{2}\right)-\left(x+y\right)^{2}$$

Use the distributive property to multiply 9 by x^{2}-2xy+y^{2}.

$$9x^{2}-18xy+9y^{2}-\left(x+y\right)^{2}$$

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

$$9x^{2}-18xy+9y^{2}-\left(x^{2}+2xy+y^{2}\right)$$

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

$$9x^{2}-18xy+9y^{2}-x^{2}-2xy-y^{2}$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}-18xy+9y^{2}-2xy-y^{2}$$

Combine -18xy and -2xy to get -20xy.

$$8x^{2}-20xy+9y^{2}-y^{2}$$

Combine 9y^{2} and -y^{2} to get 8y^{2}.

$$8x^{2}-20xy+8y^{2}$$

Expand

$$8x^{2}-20xy+8y^{2}$$

Solution Steps

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

$$9\left(x^{2}-2xy+y^{2}\right)-\left(x+y\right)^{2}$$

Use the distributive property to multiply 9 by x^{2}-2xy+y^{2}.

$$9x^{2}-18xy+9y^{2}-\left(x+y\right)^{2}$$

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

$$9x^{2}-18xy+9y^{2}-\left(x^{2}+2xy+y^{2}\right)$$

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

$$9x^{2}-18xy+9y^{2}-x^{2}-2xy-y^{2}$$

Combine 9x^{2} and -x^{2} to get 8x^{2}.

$$8x^{2}-18xy+9y^{2}-2xy-y^{2}$$

Combine -18xy and -2xy to get -20xy.

$$8x^{2}-20xy+9y^{2}-y^{2}$$

Combine 9y^{2} and -y^{2} to get 8y^{2}.

$$8x^{2}-20xy+8y^{2}$$