Coefficient zero by design (proof)

Questions that ask to prove or show that a specific coefficient is zero for a given expression with parameters, rather than finding the parameter value.

2 questions · Standard +0.6

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

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CAIE P1 2015 November Q1

3 marks Standard +0.3

1 In the expansion of \(\left( 1 - \frac { 2 x } { a } \right) ( a + x ) ^ { 5 }\), where \(a\) is a non-zero constant, show that the coefficient of \(x ^ { 2 }\) is zero.

CAIE P1 Specimen Q1

3 marks Standard +0.8

1 In the expansion of \(\left( 1 - \frac { 2 x } { a } \right) ( a + x ) ^ { 5 }\), where \(a\) is a non-zero constant, show that the coefficient of \(x ^ { 2 }\) is zero.