Find constant from coefficient condition

Questions that give the coefficient of a specific term in the sum or difference of two binomial expansions and ask to find an unknown constant.

5 questions · Moderate -0.1

1.04a Binomial expansion: (a+b)^n for positive integer n

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CAIE P1 2022 November Q4

6 marks Standard +0.3

4 The coefficient of \(x ^ { 2 }\) in the expansion of \(\left( 1 + \frac { 2 } { p } x \right) ^ { 5 } + ( 1 + p x ) ^ { 6 }\) is 70 .
Find the possible values of the constant \(p\).

CAIE P1 2011 June Q1

5 marks Moderate -0.5

1 The coefficient of \(x ^ { 3 }\) in the expansion of \(( a + x ) ^ { 5 } + ( 1 - 2 x ) ^ { 6 }\), where \(a\) is positive, is 90 . Find the value of \(a\).

CAIE P1 2018 June Q1

5 marks Moderate -0.3

1 The coefficient of \(x ^ { 2 }\) in the expansion of \(\left( 2 + \frac { x } { 2 } \right) ^ { 6 } + ( a + x ) ^ { 5 }\) is 330 . Find the value of the constant \(a\).

CAIE P1 2016 November Q2

4 marks Moderate -0.3

The coefficient of \(x^3\) in the expansion of \((1 - 3x)^6 + (1 + ax)^5\) is 100. Find the value of the constant \(a\). [4]

CAIE P3 2018 June Q1

5 marks Standard +0.3

The coefficient of \(x^2\) in the expansion of \(\left(2 + \frac{x}{2}\right)^6 + (a + x)^5\) is 330. Find the value of the constant \(a\). [5]