Solve 3(x+y)^2-6(x+y)

$$3 ( x + y ) ^ { 2 } - 6 ( x + y )$$

Evaluate

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

Solution Steps

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

$$3\left(x^{2}+2xy+y^{2}\right)-6\left(x+y\right)$$

Use the distributive property to multiply 3 by x^{2}+2xy+y^{2}.

$$3x^{2}+6xy+3y^{2}-6\left(x+y\right)$$

Use the distributive property to multiply -6 by x+y.

$$3x^{2}+6xy+3y^{2}-6x-6y$$

Expand

$$3x^{2}+6xy-6x+3y^{2}-6y$$

Solution Steps

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

$$3\left(x^{2}+2xy+y^{2}\right)-6\left(x+y\right)$$

Use the distributive property to multiply 3 by x^{2}+2xy+y^{2}.

$$3x^{2}+6xy+3y^{2}-6\left(x+y\right)$$

Use the distributive property to multiply -6 by x+y.

$$3x^{2}+6xy+3y^{2}-6x-6y$$