Edexcel C4 — Question 2

Exam BoardEdexcel
ModuleC4 (Core Mathematics 4)
TopicGeneralised Binomial Theorem
TypeProduct of separate expansions

2. (a) Expand \(( 1 - 3 x ) ^ { - 2 } , | x | < \frac { 1 } { 3 }\), in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), simplifying each coefficient.
(b) Hence, or otherwise, show that for small \(x\), $$\left( \frac { 2 - x } { 1 - 3 x } \right) ^ { 2 } \approx 4 + 20 x + 85 x ^ { 2 } + 330 x ^ { 3 }$$