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Question
Evaluate the
(v) \[\left( 3 + \sqrt{2} \right)^5 - \left( 3 - \sqrt{2} \right)^5\]
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Solution
(v) \[(3 + \sqrt{2} )^5 - (3 - \sqrt{2} )^5 \]
\[ = 2\left[^{5}{}{C}_1 \times 3^4 \times (\sqrt{2} )^1 + ^{5}{}{C}_3 \times 3^2 \times (\sqrt{2} )^3 + ^{5}{}{C}_5 \times 3^0 \times (\sqrt{2} )^5 \right]\]
\[= 2[5 \times 81 \times \sqrt{2} + 10 \times 9 \times 2\sqrt{2} + 4\sqrt{2}]\]
\[ = 2\sqrt{2}(405 + 180 + 4) = 1178\sqrt{2}\]
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