Solve 3left(x+yright)-9left(x+yright)^2

$$3 \left( x+y \right) -9 { \left(x+y \right) }^{ 2 }$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 3 by x+y.

$$3x+3y-9\left(x+y\right)^{2}$$

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

$$3x+3y-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$3x+3y-9x^{2}-18xy-9y^{2}$$

Expand

$$3y-9y^{2}+3x-18xy-9x^{2}$$

Solution Steps

Use the distributive property to multiply 3 by x+y.

$$3x+3y-9\left(x+y\right)^{2}$$

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

$$3x+3y-9\left(x^{2}+2xy+y^{2}\right)$$

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

$$3x+3y-9x^{2}-18xy-9y^{2}$$