Question 3 - A-Level Maths

Exam Board	OCR
Module	C2 (Core Mathematics 2)
Year	2013
Session	June
Topic	Binomial Theorem (positive integer n)
Type	Product with unknown constant to determine

Find and simplify the first three terms in the expansion of \(( 2 + 5 x ) ^ { 6 }\) in ascending powers of \(x\).
In the expansion of \(( 3 + c x ) ^ { 2 } ( 2 + 5 x ) ^ { 6 }\), the coefficient of \(x\) is 4416. Find the value of \(c\).