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

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

Evaluate

$$\left(x-11y\right)\left(7x-5y\right)$$

Solution Steps

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

$$16\left(x^{2}-4xy+4y^{2}\right)-9\left(x+y\right)^{2}$$

Use the distributive property to multiply 16 by x^{2}-4xy+4y^{2}.

$$16x^{2}-64xy+64y^{2}-9\left(x+y\right)^{2}$$

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

$$16x^{2}-64xy+64y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$16x^{2}-64xy+64y^{2}-9x^{2}-18xy-9y^{2}$$

Combine 16x^{2} and -9x^{2} to get 7x^{2}.

$$7x^{2}-64xy+64y^{2}-18xy-9y^{2}$$

Combine -64xy and -18xy to get -82xy.

$$7x^{2}-82xy+64y^{2}-9y^{2}$$

Combine 64y^{2} and -9y^{2} to get 55y^{2}.

$$7x^{2}-82xy+55y^{2}$$

Expand

$$7x^{2}-82xy+55y^{2}$$

Solution Steps

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

$$16\left(x^{2}-4xy+4y^{2}\right)-9\left(x+y\right)^{2}$$

Use the distributive property to multiply 16 by x^{2}-4xy+4y^{2}.

$$16x^{2}-64xy+64y^{2}-9\left(x+y\right)^{2}$$

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

$$16x^{2}-64xy+64y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$16x^{2}-64xy+64y^{2}-9x^{2}-18xy-9y^{2}$$

Combine 16x^{2} and -9x^{2} to get 7x^{2}.

$$7x^{2}-64xy+64y^{2}-18xy-9y^{2}$$

Combine -64xy and -18xy to get -82xy.

$$7x^{2}-82xy+64y^{2}-9y^{2}$$

Combine 64y^{2} and -9y^{2} to get 55y^{2}.

$$7x^{2}-82xy+55y^{2}$$