Multiply: (7x + y) by (x + 5y)

To multiply, we will use distributive law as follows:

$(7 x+y)(x+5 y)$

$=7 x(x+5 y)+y(x+5 y)$

$=7 x^{2}+35 x y+x y+5 y^{2}$

$=7 x^{2}+36 x y+5 y^{2}$

Thus, the answer is $7 x^{2}+36 x y+5 y^{2}$.