Solve 3(x+y)^2+(x+y)-4

$$3 ( x + y ) ^ { 2 } + ( x + y ) - 4$$

Expand

$$3x^{2}+6xy+x+3y^{2}+y-4$$

Solution Steps

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

$$3\left(x^{2}+2xy+y^{2}\right)+x+y-4$$

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

$$3x^{2}+6xy+3y^{2}+x+y-4$$

Evaluate

$$3\left(x+y\right)^{2}+x+y-4$$

Solution Steps

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

$$3\left(x^{2}+2xy+y^{2}\right)+x+y-4$$

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

$$3x^{2}+6xy+3y^{2}+x+y-4$$