Question

In the expansion of (2x + a)^3, the co-efficient of the x^2 term is -36. So a must equal

A -6
B 6
C -9
D 9
E -3

Show me working out thanks.

Answer 1

We know that
\[(a+b)^3= a^3+3a^2b+3ab^2+b^3\]
so her
\[(2x+a)^3=8x^3+12x^2a+6xa^2+a^3\]
coefficient of x^2
\[(2x+a)^3=8x^3+\underline{12x^2a}+6xa^2+a^3\]
12a
it's given
12a=-36
so

a=-3

Answer 2

thanks.