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)
Write down the expansion of \(( 2 - x ) ^ { 3 }\).
Hence show that \(( 2 + x ) ^ { 3 } - ( 2 - x ) ^ { 3 } = 24 x + 2 x ^ { 3 }\).
Hence show that the curve with equation
$$y = ( 2 + x ) ^ { 3 } - ( 2 - x ) ^ { 3 }$$
has no stationary points.