Standard +0.3 This is a straightforward binomial expansion problem requiring students to expand (a+x)^5, multiply by the linear factor, collect x^2 terms, and show they sum to zero. While it involves multiple steps and algebraic manipulation, it's a standard textbook exercise with no novel insight required—slightly easier than average due to its mechanical nature and the fact that students are told what to prove.
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.
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.
\hfill \mbox{\textit{CAIE P1 2015 Q1 [3]}}