Question 8 - A-Level Maths

Exam Board	CAIE
Module	P1 (Pure Mathematics 1)
Year	2013
Session	November
Topic	Binomial Theorem (positive integer n)
Type	Standard product of two binomials

Find the coefficient of \(x ^ { 8 }\) in the expansion of \(\left( x + 3 x ^ { 2 } \right) ^ { 4 }\).
Find the coefficient of \(x ^ { 8 }\) in the expansion of \(\left( x + 3 x ^ { 2 } \right) ^ { 5 }\).
Hence find the coefficient of \(x ^ { 8 }\) in the expansion of \(\left[ 1 + \left( x + 3 x ^ { 2 } \right) \right] ^ { 5 }\).