Question 11 of 20intermediate🔧 ApplyLong Answer5 marks

Find (a+b)4−(a−b)4(a + b)^4 - (a - b)^4. Hence, evaluate (3+2)4−(3−2)4(\sqrt{3} + \sqrt{2})^4 - (\sqrt{3} - \sqrt{2})^4.

(i)
Answer

8ab(a² + b²)

(ii)
Answer

406\sqrt{6}

Explanation

This question tests the application of the Binomial Theorem for positive integral indices. Students must first expand both (a+b)4(a+b)^4 and (a−b)4(a-b)^4 using the standard formula, then subtract to find a simplified expression.

The key observation is that even-powered terms cancel out while odd-powered terms double. Part (ii) requires substituting the given values into the derived formula.

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