2025 IGCSE Additional Mathematics February/March 0606/22 Q10

2025 IGCSE Additional Mathematics February/March 0606/22 Q10

10 marks

The expansion of \((ax-2)^4\left(1+\dfrac bx\right)^3\) is written in descending powers of \(x\).

The first 3 terms of this expansion are \(81x^4+999x^3+cx^2\).

It is given that \(a\), \(b\) and \(c\) are positive integers.

Find the values of \(a\), \(b\) and \(c\).[10]

Solution:

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Answer:\(a=3,\quad b=5,\quad c=3051\)

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