How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?

# Number of terms in expansion (TOMATO objective 102)

Problem:

The number of terms in the expression of

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

A) 4;

B) 5;

C) 6;

D) 7;

Solution:

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

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

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

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