Easy -1.2 This is a straightforward application of the binomial theorem for positive integer n=5, requiring only direct substitution into the formula and basic algebraic simplification. Part (b) involves simple polynomial multiplication and truncation, which is routine bookwork with no problem-solving element. Well below average difficulty for A-level.
2. (a) Find the first 4 terms, in ascending powers of \(x\), of the binomial expansion of \(( 1 - 2 x ) ^ { 5 }\). Give each term in its simplest form.
(b) If \(x\) is small, so that \(x ^ { 2 }\) and higher powers can be ignored, show that
$$( 1 + x ) ( 1 - 2 x ) ^ { 5 } \approx 1 - 9 x$$
DU
Correct binomial structure with increasing powers of \(x\). Accept \(^5C_1\), \(\binom{5}{1}\). Condone invisible brackets and using \(2x\) instead of \(-2x\)
\(40x^2\)
A1
\(-80x^3\)
A1
Allow commas between terms. Allow recovery from invisible brackets
2. (a) Find the first 4 terms, in ascending powers of $x$, of the binomial expansion of $( 1 - 2 x ) ^ { 5 }$. Give each term in its simplest form.\\
(b) If $x$ is small, so that $x ^ { 2 }$ and higher powers can be ignored, show that
$$( 1 + x ) ( 1 - 2 x ) ^ { 5 } \approx 1 - 9 x$$
DU\\
\hfill \mbox{\textit{Edexcel C2 2007 Q2 [6]}}