Verified Answer :

mathmate

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

JeanaShupp

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

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