Find, in ascending powers of $x$, the first three terms in the expansion of \({{\left( 2-\frac{x}{

Question

Find, in ascending powers of $x$, the first three terms in the expansion of ${{\left( 2-\frac{x}{2} \right)}^{6}}.$ Hence, find the coefficient of ${{x}^{2}}$ in the expansion of ${{\left( x+1 \right)}^{2}}{{\left( 2-\frac{x}{2} \right)}^{6}}.$

Accepted Answer

First three terms: $64-96x+60x^2$ Coefficient of $x^2$: $-68$

Binomial Theorem - Binomial Expansion for Positive Integer Powers

Binomial Theorem - Binomial Expansion for Positive Integer Powers

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