Given that the coefficient of ${{x}^{2}}$ in the expansion of \({{\left( 1-2x \right)}^{2}}{{\left

Question

Given that the coefficient of ${{x}^{2}}$ in the expansion of ${{\left( 1-2x \right)}^{2}}{{\left( 1+px \right)}^{7}}$ is $32$, find the possible values of the constant $p$. Hence find the coefficient of ${{x}^{2}}$ in the expansion of ${{\left( 1-x \right)}^{2}}{{\left( 1+\frac{px}{2} \right)}^{7}}.$

Accepted Answer

(i) $p=-\frac{2}{3}$ or $p=2$ (ii) $8$

Binomial Theorem - Coefficients in Products of Binomial Expansions

Binomial Theorem - Coefficients in Products of Binomial Expansions

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