Question

II. Simplify: (5 marks problems) 1. \( (\sqrt{3}+1)^{5}-(\sqrt{3}-1)^{5} \) 2. \( (1+\sqrt{5})^{5}-(1-\sqrt{5})^{5} \) 3. \( (3+\sqrt{2})^{4}+(3-\sqrt{2})^{4} \) 4. \( (\sqrt{2}+1)^{6}-(\sqrt{2}-1)^{6} \)

Answer 1

In the above binomial expansion, the terms at the odd position will get eliminated. We would be left with

2(⁵C₁​(\(\sqrt 3\)​)⁴+⁵C₃​(\(\sqrt 3\)​)²+⁵C₅​)

=2(5(3²)+10(3)+1)

=2(45+30+1)

=2(76)

=152