Easy -1.2 This is a straightforward application of the binomial theorem with n=3 (very small power) requiring only expansion and simplification of terms involving x and 1/x. It's a routine C1 exercise with minimal steps and no problem-solving insight needed, making it easier than average.
B1 for both of \(x^3\) and \(\dfrac{125}{x^3}\) or \(125x^{-3}\) isw; and M1 for 1 3 3 1 soi; A1 for each of \(15x\) and \(\dfrac{75}{x}\) or \(75x^{-1}\) isw; or SC2 for completely correct unsimplified answer
## Question 8:
| Answer | Mark | Guidance |
|--------|------|----------|
| $x^3 + 15x + \dfrac{75}{x} + \dfrac{125}{x^3}$ www isw or $x^3 + 15x + 75x^{-1} + 125x^{-3}$ www isw | 4 | B1 for **both** of $x^3$ **and** $\dfrac{125}{x^3}$ or $125x^{-3}$ isw; and M1 for 1 3 3 1 soi; A1 for **each** of $15x$ **and** $\dfrac{75}{x}$ or $75x^{-1}$ isw; **or** SC2 for completely correct unsimplified answer |