Write down and simplify, the first three terms of the expansion in ascending powers of $x$, \({{\l

Question

Write down and simplify, the first three terms of the expansion in ascending powers of $x$, ${{\left( 2-3x \right)}^{10}}$, ${{\left( \frac{x}{2}+1 \right)}^{10}}$, Hence, find the coefficient of ${{x}^{2}}$ in the expansion of ${{\left( \frac{4-4x-3{{x}^{2}}}{2} \right)}^{10}}$.

Accepted Answer

(i) $1024-15360x+103680x^2+\cdots$ (ii) $1+5x+\frac{45}{4}x^2+\cdots$ (iii) $38400$

Binomial Theorem - Binomial Expansion for Positive Integer Powers

Binomial Theorem - Binomial Expansion for Positive Integer Powers

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