Question

Find the answer to (x + y + 2)( y + 1)

Answer 1

Answer: $(x + y + 2)( y + 1)=xy+y^2+3y+x+2$

Step-by-step explanation:

The given expression: $(x + y + 2)( y + 1)$

Using left distributive property:

$a(b+c)=ab+ac$, where a, b, c are any arbitrary expressions.

$\Rightarrow (x + y + 2)( y + 1)=(x+y+2)y+(x+y+2)(1)\\\\=$

Using right distributive property:

$(b+c)a=ba+ca$, where a, b, c are any arbitrary expressions.

$\Rightarrow(x+y+2)y+(x+y+2)(1)=xy+y^2+2y+x+y+2=xy+y^2+3y+x+2$

Hence, $(x + y + 2)( y + 1)=xy+y^2+3y+x+2$

Answer 2

I assume the question asks to expand the expression to individual terms.
There are different ways to approach this, all based on FOIL or similar methods.
I prefer to split it into two parts, as follows:
(x+y+2)(y+1)
=x(y+1)+(y+2)(y+1)
=xy+x+y^2+3y+2