From the question
We are to expand the expression
[tex](x+7)(x+1)[/tex]This is done as follows
[tex](x+7)(x+1)=x(x+1)+7(x+1)[/tex]By expanding further we have
[tex]\begin{gathered} (x+7)(x+1) \\ =x\mleft(x+1\mright)+7\mleft(x+1\mright) \\ =x^2+x+7x+7 \\ =x^2+8x+7 \end{gathered}[/tex]Therefore the answer is
[tex]x^2+8x+7[/tex]