Solve 16(x-y)^2-9(x+y)

$$16 ( x - y ) ^ { 2 } - 9 ( x + y )$$

Evaluate

$$16\left(x-y\right)^{2}-9x-9y$$

Solution Steps

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

$$16\left(x^{2}-2xy+y^{2}\right)-9\left(x+y\right)$$

Use the distributive property to multiply 16 by x^{2}-2xy+y^{2}.

$$16x^{2}-32xy+16y^{2}-9\left(x+y\right)$$

Use the distributive property to multiply -9 by x+y.

$$16x^{2}-32xy+16y^{2}-9x-9y$$

Expand

$$16x^{2}-32xy-9x+16y^{2}-9y$$

Solution Steps

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

$$16\left(x^{2}-2xy+y^{2}\right)-9\left(x+y\right)$$

Use the distributive property to multiply 16 by x^{2}-2xy+y^{2}.

$$16x^{2}-32xy+16y^{2}-9\left(x+y\right)$$

Use the distributive property to multiply -9 by x+y.

$$16x^{2}-32xy+16y^{2}-9x-9y$$