Number of terms in expansion (TOMATO objective 102)

Problem:

The number of terms in the expression of

$latex [(a+3b)^2 (a-3b)^2]^2 $

A) 4;

B) 5;

C) 6;

D) 7;

Solution:

$latex [(a+3b)^2  (a-3b)^2]^2 $

$latex = [\{(a+3b)(a-3b)\}^2]^2 $

$latex = \{ (a^2  -9b^2)^2\}^2 = (a^2 - 9b^2)^4 $

By Binomial Theorem, the given expression contains 5 terms (since $latex (x +y)^n $ has n+1 terms in general).

Answer: B) 5;