Write down the first three terms in the expansion, in descending powers of $x$, of \( \left(x^2 +

Question

Write down the first three terms in the expansion, in descending powers of $x$, of $ \left(x^2 + \frac{m}{x} \right)^9$, where $m$ is an integer.[2] Given that the coefficient of $x^3$ in the expansion of $ \left(x^2 + \frac{m}{x} \right)^9$ is $-126$, show that $m = -1$,[3] hence, find the term independent of $x$ in the expression of $ \left(2 - \frac{1}{x^3} \right) \left(x^2 + \frac{m}{x} \right)^9$.[4]

Accepted Answer

(a) $x^{18}+9mx^{15}+36m^2x^{12}$ (b)(i) $m=-1$ (shown) (b)(ii) $294$

2024 FMSS PRELIMS P2 Q7

2024 FMSS PRELIMS P2 Q7

Video Solution:

Solution:

Solution locked