Standard binomial expansion coefficient

2

1. Determine the value of \(\frac { 100 ! } { 98 ! }\).
2. Find the coefficient of \(x ^ { 98 }\) in the expansion of \(( 1 + x ) ^ { 100 }\).

2 Find the coefficient of \(x ^ { 4 }\) in the binomial expansion of \(( x - 3 ) ^ { 5 }\).

7 Determine the coefficient of \(x ^ { 5 }\) in the expansion of \(( 3 - 2 x ) ^ { 7 }\).

1 Find the coefficient of \(x ^ { 4 }\) in the expansion of \(( 1 + 3 x ) ^ { 6 }\).

5. Find the coefficient of the term in \(x ^ { 7 }\) of the binomial expansion of $$\left( \frac { 3 } { 8 } + 4 x \right) ^ { 12 }$$ giving your answer in simplest form.
(3) \section*{(Total for Question 5 is 3 marks)}

6

1. Find the coefficient of \(x ^ { 4 }\) in the expansion of \(( 3 x - 2 ) ^ { 10 }\).
2. In the expansion of \(( 1 + 2 x ) ^ { n }\), where \(n\) is a positive integer, the coefficients of \(x ^ { 7 }\) and \(x ^ { 8 }\) are equal. Find the value of \(n\).
3. Find the coefficient of \(x ^ { 3 }\) in the expansion of \(\frac { 1 } { \sqrt { 4 + x } }\).

8 Calculate \({ } ^ { 6 } \mathrm { C } _ { 3 }\).
Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 1 - 2 x ) ^ { 6 }\).

1 Find the coefficient of the \(x\) term in the binomial expansion of \(( 3 + x ) ^ { 4 }\) Circle your answer. 122754108

3 Find the coefficient of the \(x ^ { 3 }\) term in the expansion of \(\left( 3 x + \frac { 1 } { 2 } \right) ^ { 4 }\)

1 Find the coefficient of \(x ^ { 7 }\) in the expansion of \(( 2 x - 3 ) ^ { 7 }\)
Circle your answer.
-2187-128 2128

2 Find the coefficient of \(x ^ { 2 }\) in the expansion of \(( 1 + 2 x ) ^ { 7 }\)
Circle your answer. 4242184
\includegraphics[max width=\textwidth, alt={}, center]{5e475c96-6bbb-44fb-a411-706dac20e2d6-03_1442_1168_219_365} Find the total shaded area. Circle your answer.
-68 60686128