Find the coefficient of $$$x^{2}$$$ in the expansion of $$$\left(2+3 x^{2}\right)\left(x-\frac{2}{x}\right)^{6}$$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_12 Year：2020 Question No：1(b)

Answer:

Constant term in $\left(x-\frac{2}{x}\right)^{6}=20 x^{3} \times\left(\frac{-2}{x}\right)^{3}(-160)$
Coefficient of $x^{2}$ in $(2+3 x)\left(x-\frac{2}{x}\right)^{6}=120-480=-360$

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.)

Answer:

Knowledge points:

Solution:

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