Solve 2(x+y)^2+3(x+y)+1=

$$2 ( x + y ) ^ { 2 } + 3 ( x + y ) + 1 =$$

Evaluate

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

Solution Steps

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

$$2\left(x^{2}+2xy+y^{2}\right)+3\left(x+y\right)+1$$

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

$$2x^{2}+4xy+2y^{2}+3\left(x+y\right)+1$$

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

$$2x^{2}+4xy+2y^{2}+3x+3y+1$$

Expand

$$2x^{2}+4xy+3x+2y^{2}+3y+1$$

Solution Steps

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

$$2\left(x^{2}+2xy+y^{2}\right)+3\left(x+y\right)+1$$

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

$$2x^{2}+4xy+2y^{2}+3\left(x+y\right)+1$$

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

$$2x^{2}+4xy+2y^{2}+3x+3y+1$$