Solve 2(x+y)^2-9(x+y)-5

$$2 ( x + y ) ^ { 2 } - 9 ( x + y ) - 5$$

Evaluate

$$\left(x+y-5\right)\left(2x+2y+1\right)$$

Solution Steps

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

$$2\left(x^{2}+2xy+y^{2}\right)-9\left(x+y\right)-5$$

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

$$2x^{2}+4xy+2y^{2}-9\left(x+y\right)-5$$

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

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

Expand

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

Solution Steps

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

$$2\left(x^{2}+2xy+y^{2}\right)-9\left(x+y\right)-5$$

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

$$2x^{2}+4xy+2y^{2}-9\left(x+y\right)-5$$

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

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