AQA C2 2005 January — Question 6

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2005
SessionJanuary
TopicBinomial Theorem (positive integer n)
TypeSimplify to standard form

6
    1. Using the binomial expansion, or otherwise, express \(( 2 + x ) ^ { 3 }\) in the form \(8 + a x + b x ^ { 2 } + x ^ { 3 }\), where \(a\) and \(b\) are integers. (3 marks)
    2. Write down the expansion of \(( 2 - x ) ^ { 3 }\).
  1. Hence show that \(( 2 + x ) ^ { 3 } - ( 2 - x ) ^ { 3 } = 24 x + 2 x ^ { 3 }\).
  2. Hence show that the curve with equation $$y = ( 2 + x ) ^ { 3 } - ( 2 - x ) ^ { 3 }$$ has no stationary points.