Easy -1.2 This is a straightforward application of the binomial theorem requiring only direct substitution into the formula for the first three terms of (a+b)^n with n=5. It's purely procedural with no problem-solving element, making it easier than average, though slightly more involved than basic index law recall due to the arithmetic required.
Find the first three terms, in ascending powers of \(x\), of the binomial expansion of \(( 3 + 2 x ) ^ { 5 }\), giving each term in its simplest form.
(4)
$(3+2x)^5 = (3)^5 + \binom{5}{1}3^4 \cdot (2x) + \binom{5}{2}3^3(2x)^2 + \cdots = 243+810x+1080x^2$ | M1, B1, A1, A1 | (4 marks) | M1: Use of binomial leading to correct expression for $x$ or $x^2$ term; can be implied. $\binom{n}{r}$ notation is acceptable.
Find the first three terms, in ascending powers of $x$, of the binomial expansion of $( 3 + 2 x ) ^ { 5 }$, giving each term in its simplest form.\\
(4)\\
\hfill \mbox{\textit{Edexcel C2 2005 Q1 [4]}}