Problem: The number of terms in the expansion of [(a+3b)2(a−3b)2]2\left[(a+3 b)^{2}(a-3 b)^{2}\right]^{2}[(a+3b)2(a−3b)2]2 when simplified is:
Answer Choices:
A. 444 B. 555 C. 666 D. 777 E. 888
Solution:
The binomial expansion of (x+y)n(x+y)^{n}(x+y)n has n+1n+1n+1 terms. Thus
[(a+3b)2(a−3b)2]2=(a2−9b2)4\left[(a+3 b)^{2}(a-3 b)^{2}\right]^{2}=\left(a^{2}-9 b^{2}\right)^{4} [(a+3b)2(a−3b)2]2=(a2−9b2)4
has 4+1=54+1=\boxed{5}4+1=5 terms.