Easy -1.2 This is a straightforward application of the binomial theorem requiring only substitution into the formula and simplification of coefficients. It's a standard C2 exercise with no problem-solving element—students simply need to recall the binomial expansion formula and perform routine arithmetic with the given values a=2, b=-x/2, n=8.
3. Find the first 4 terms, in ascending powers of \(x\), of the binomial expansion of
$$\left( 2 - \frac { 1 } { 2 } x \right) ^ { 8 }$$
giving each term in its simplest form.
Two binomial coefficients must be correct and with correct power of \(x\); accept \({}^8C_1\) or \(\binom{8}{1}\) or 8 as coefficient, and \({}^8C_2\) or \(\binom{8}{2}\) or 28
\(=(256)-512x+448x^2-224x^3\)
A1, A1
First A1: any two of final three terms correct (allow \(+-\) instead of \(-\)); Second A1: all three final terms correct and simplified
## Question 3:
### Way 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| $\left(2-\frac{1}{2}x\right)^8 = 2^8+\binom{8}{1}\cdot2^7\left(-\frac{1}{2}x\right)+\binom{8}{2}2^6\left(-\frac{1}{2}x\right)^2+\binom{8}{3}2^5\left(-\frac{1}{2}x\right)^3$ | — | — |
| First term of 256 | B1 | First term must be 256 |
| $\left({}^8C_1\times\ldots\times x\right)+\left({}^8C_2\times\ldots\times x^2\right)+\left({}^8C_3\times\ldots\times x^3\right)$ | M1 | Two binomial coefficients must be correct and with correct power of $x$; accept ${}^8C_1$ or $\binom{8}{1}$ or 8 as coefficient, and ${}^8C_2$ or $\binom{8}{2}$ or 28 |
| $=(256)-512x+448x^2-224x^3$ | A1, A1 | First A1: any two of final three terms correct (allow $+-$ instead of $-$); Second A1: all three final terms correct and simplified |
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3. Find the first 4 terms, in ascending powers of $x$, of the binomial expansion of
$$\left( 2 - \frac { 1 } { 2 } x \right) ^ { 8 }$$
giving each term in its simplest form.\\
\hfill \mbox{\textit{Edexcel C2 2013 Q3 [4]}}