By considering the general term in the binomial expansion of $\left(x^4-\frac{1}{kx^2}\right)^6$,

Question

By considering the general term in the binomial expansion of $\left(x^4-\frac{1}{kx^2}\right)^6$, where $k$ is a positive constant, explain why there are only even powers of $x$ in this expansion.[3] Given that the term independent of $x$ in the binomial expansion of $\left(x^4-\frac{1}{kx^2}\right)^6$ is $\frac{5}{27}$, show that $k$ is $3$.[2] Hence find the term independent of $x$ in $ \left(2-3x^6 \right) \left(x^4-\frac{1}{kx^2} \right)^6$.[4]

Accepted Answer

(a) $24-6r$ is always even (b) $k=3$ (c) $\frac{4}{9}$

2025 SCGS PRELIMS P2 Q6

2025 SCGS PRELIMS P2 Q6

Video Solution:

Solution:

Solution locked