Question 3 - A-Level Maths

Exam Board	OCR
Module	C2 (Core Mathematics 2)
Year	2010
Session	June
Topic	Binomial Theorem (positive integer n)
Type	Binomial times quadratic coefficient

Find and simplify the first four terms in the binomial expansion of \(\left( 1 + \frac { 1 } { 2 } x \right) ^ { 10 }\) in ascending powers of \(x\).
Hence find the coefficient of \(x ^ { 3 }\) in the expansion of \(\left( 3 + 4 x + 2 x ^ { 2 } \right) \left( 1 + \frac { 1 } { 2 } x \right) ^ { 10 }\).