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Question
The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` is ______.
Solution
The coefficient of a–6b4 in the expansion of `(1/a - (2b)/3)^10` is `1120/27`.
Explanation:
The given expansion is `(1/a - (2b)/3)^10`
From a–6b4
We can take r = 4
∴ T5 = T4+1
= `""^10"C"_4 (1/a)^(10 - 4) (- (2b)/3)^4`
= `""^10"C"_4 (1/a)^6 ((-2)/3)^4 * b^4`
= `(10*9*8*7)/(4*3*2*1) xx 16/81 * a^-6b^4`
= `210 xx 16/81 a^-6b^4`
= `1120/27 a^-6b^4`
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