Find the first $4$ terms in the expansion of $ \left(\frac{a}{x}+3x^2 \right)^6$ in ascending po

Question

Find the first $4$ terms in the expansion of $ \left(\frac{a}{x}+3x^2 \right)^6$ in ascending powers of $x$, simplifying each term.[3] Given that there is no terms in $x^3$ in the expansion of $ \left(2x^3-1\right)\left(\frac{a}{x}+3x^2 \right)^6$, find the value of the positive constant $a$.[2]

Accepted Answer

(a) $\frac{a^6}{x^6}+\frac{18a^5}{x^3}+135a^4+540a^3x^3+\cdots$ (b) $a=2$

2025 MSHS PRELIMS P1 Q5

2025 MSHS PRELIMS P1 Q5

Solution:

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