Option D:
[tex](x+y+2)(y+1)=y^2+xy+x+3y+2[/tex]
Solution:
Given expression:
[tex](x+y+2)(y+1)[/tex]
To expand the expression:
[tex](x+y+2)(y+1)[/tex]
Multiply each term of the first term with each term of the second term.
[tex](x+y+2)(y+1)=x(y+1)+y(y+1)+2(y+1)[/tex]
[tex]=xy+x+y^2+y+2y+2[/tex]
[tex]=xy+x+y^2+3y+2[/tex]
[tex]=y^2+xy+x+3y+2[/tex]
[tex](x+y+2)(y+1)=y^2+xy+x+3y+2[/tex]
Hence option D is the correct answer.
