Product with linear term

Questions where a simple linear term (a+bx) or (a-bx) is multiplied by a binomial expansion (1+cx)^n, requiring straightforward multiplication of the linear factor with the first few terms of the expansion.

6 questions

CAIE P3 2013 June Q2

2 Expand \(\frac { 1 + 3 x } { \sqrt { } ( 1 + 2 x ) }\) in ascending powers of \(x\) up to and including the term in \(x ^ { 2 }\), simplifying the coefficients.

CAIE P3 2019 June Q1

1 Find the coefficient of \(x ^ { 3 }\) in the expansion of \(( 3 - x ) ( 1 + 3 x ) ^ { \frac { 1 } { 3 } }\) in ascending powers of \(x\).

CAIE P3 2008 November Q2

2 Expand \(( 1 + x ) \sqrt { } ( 1 - 2 x )\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), simplifying the coefficients.

CAIE P3 2016 November Q2

2 Expand \(( 2 - x ) ( 1 + 2 x ) ^ { - \frac { 3 } { 2 } }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), simplifying the coefficients.

CAIE P3 2024 June Q1

1 Expand \(( 3 + x ) ( 1 - 2 x ) ^ { \frac { 1 } { 2 } }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\), simplifying the coefficients.

SPS SPS FM 2025 February Q2

2. (i) Find the first three terms in the expansion of \(( 1 - 2 x ) ^ { - \frac { 1 } { 2 } }\) in ascending powers of \(x\), where \(| x | < \frac { 1 } { 2 }\).
(ii) Hence find the coefficient of \(x ^ { 2 }\) in the expansion of \(\frac { x + 3 } { \sqrt { 1 - 2 x } }\).
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