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Binomial Theorem Miscellaneous Exercise on Chapter 7 Solutions
- Q1: If (a) and (b) are distinct integers, prove that (a – b) is a factor of (a^{n} – b^{n}), whenever (n) is a positive integer. [Hint write (a^{n} = (a – b + b)^{n}) and expand]
- Q2: Evaluate ((\sqrt{3} + \sqrt{2})^{6} – (\sqrt{3} – \sqrt{2})^{6}).
- Q3: Find the value of ((a^{2} + \sqrt{a^{2}-1})^{4} + (a^{2} - \sqrt{a^{2}-1})^{4}).
- Q4: Find an approximation of ((0.99)^{5}) using the first three terms of its expansion.
- Q5: Expand using Binomial Theorem (1 + \frac{x}{2} - \frac{2}{x})^{4}, (x \neq 0).
- Q6: Find the expansion of ((3x^{2} – 2ax + 3a^{2})^{3}) using binomial theorem.
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