Moderate -0.3 This is a straightforward two-part binomial expansion question requiring standard technique. Part (i) is routine application of the binomial theorem with numerical coefficients. Part (ii) requires the simple substitution y = x - x², then collecting terms up to x³. While part (ii) involves some algebraic manipulation and careful term collection, it's a standard textbook exercise with no novel insight required, making it slightly easier than average.
3. (i) Expand \(( 2 + y ) ^ { 6 }\) in ascending powers of \(y\) as far as the term in \(y ^ { 3 }\), simplifying each coefficient.
(ii) Hence expand \(\left( 2 + x - x ^ { 2 } \right) ^ { 6 }\) in ascending powers of \(x\) as far as the term in \(x ^ { 3 }\), simplifying each coefficient.
3. (i) Expand $( 2 + y ) ^ { 6 }$ in ascending powers of $y$ as far as the term in $y ^ { 3 }$, simplifying each coefficient.\\
(ii) Hence expand $\left( 2 + x - x ^ { 2 } \right) ^ { 6 }$ in ascending powers of $x$ as far as the term in $x ^ { 3 }$, simplifying each coefficient.\\
\hfill \mbox{\textit{OCR C2 Q3 [7]}}