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Question
Evaluate the
(vii) \[\left( \sqrt{3} + 1 \right)^5 - \left( \sqrt{3} - 1 \right)^5\]
Solution
(vii)
\[(\sqrt{3} + 1 )^5 - (\sqrt{3} - 1 )^5 \]
\[ = 2[ ^{5}{}{C}_1 \times (\sqrt{3} )^4 + ^{5}{}{C}_3 \times (\sqrt{3} )^2 +^{5}{}{C}_5 \times (\sqrt{3} )^0 ]\]
\[ = 2[5 \times 9 + 10 \times 3 + 1]\]
\[ = 2 \times 76 = 152\]
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