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

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

Evaluate

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

Solution Steps

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

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

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

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

Expand

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

Solution Steps

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

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

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

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