jmc

Question

When the product (3x+2y+1)(x+4y+5) is expanded, what is the sum of the coefficients of the terms which contain a nonzero power of y?

Accepted Answer

We multiply out using the distributive property:

== (3 x + 2 y + 1) (x + 4 y + 5) = 3 x (x + 4 y + 5) + 2 y (x + 4 y + 5) + 1 (x + 4 y + 5) = 3 x^{2} + 12 x y + 15 x + 2 x y + 8 y^{2} + 10 y + x + 4 y + 5 = 3 x^{2} + 14 x y + 16 x + 8 y^{2} + 14 y + 5.

Those terms which contain some power of

y

are

14 x y

,

8 y^{2}

, and

14 y

, and the sum of the coefficients is

14 + 8 + 14 = 36

.