Binomial Theorem - Coefficients in Products of Binomial Expansions

Binomial Theorem - Coefficients in Products of Binomial Expansions

TGM Original Questions
  1. By considering the general term in the binomial expansion of \({{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{7}}\), explain why there are only three terms of negative powers of \(x\) in this expansion.
  2. Find the term independent of \(x\) in the expansion of \({{\left( 3x-{{x}^{2}} \right)}^{2}}{{\left( 2{{x}^{2}}-\frac{1}{x} \right)}^{7}}\).

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Answer:(a) Negative powers: \(-1,-4,-7\). (b) \(14\).

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