Solve 4(x-y)^2-9(x+y)^2

$$4 ( x - y ) ^ { 2 } - 9 ( x + y ) ^ { 2 }$$

Evaluate

$$-\left(x+5y\right)\left(5x+y\right)$$

Solution Steps

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

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

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

$$4x^{2}-8xy+4y^{2}-9\left(x+y\right)^{2}$$

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

$$4x^{2}-8xy+4y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$4x^{2}-8xy+4y^{2}-9x^{2}-18xy-9y^{2}$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}-8xy+4y^{2}-18xy-9y^{2}$$

Combine -8xy and -18xy to get -26xy.

$$-5x^{2}-26xy+4y^{2}-9y^{2}$$

Combine 4y^{2} and -9y^{2} to get -5y^{2}.

$$-5x^{2}-26xy-5y^{2}$$

Expand

$$-5x^{2}-26xy-5y^{2}$$

Solution Steps

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

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

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

$$4x^{2}-8xy+4y^{2}-9\left(x+y\right)^{2}$$

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

$$4x^{2}-8xy+4y^{2}-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$4x^{2}-8xy+4y^{2}-9x^{2}-18xy-9y^{2}$$

Combine 4x^{2} and -9x^{2} to get -5x^{2}.

$$-5x^{2}-8xy+4y^{2}-18xy-9y^{2}$$

Combine -8xy and -18xy to get -26xy.

$$-5x^{2}-26xy+4y^{2}-9y^{2}$$

Combine 4y^{2} and -9y^{2} to get -5y^{2}.

$$-5x^{2}-26xy-5y^{2}$$