The coefficient of $$\(x^{3}\)$$ in the expansion of $$\((1+k x)(1-2 x)^{5}\)$$ is 20 . Find the value of the constant $$\(k\)$$. ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................ ............................................................................................................................................................
Exam No：9709_w20_qp_12 Year：2020 Question No：1
Answer:
Coefficient of \(x^{3}\) in \((1-2 x)^{5}\) is \(-80\)
Coefficient of \(x^{2}\) in \((1-2 x)^{5}\) is 40
Coefficient of \(x^{3}\) in \((1+k x)(1-2 x)^{5}\) is \(40 k-80=20\)
\((k=) \frac{5}{2}\)
Coefficient of \(x^{2}\) in \((1-2 x)^{5}\) is 40
Coefficient of \(x^{3}\) in \((1+k x)(1-2 x)^{5}\) is \(40 k-80=20\)
\((k=) \frac{5}{2}\)
Knowledge points:
1.6.1 use the expansion of , where is a positive integer (Including the notations and n!) (Knowledge of the greatest term and properties of the coefficients are not required.)
Solution:
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