Question:
\( (\sqrt{3} + \sqrt{2})^4 - (\sqrt{3} - \sqrt{2})^4 = \)
\( (\sqrt{3} + \sqrt{2})^4 - (\sqrt{3} - \sqrt{2})^4 = \)
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Memorize symmetric expansion identities to avoid lengthy expansion.
Updated On: May 1, 2026
- \( 20\sqrt{6} \)
- \( 30\sqrt{6} \)
- \( 5\sqrt{10} \)
- \( 40\sqrt{6} \)
- \( 10\sqrt{6} \)
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The Correct Option is D
Solution and Explanation
Concept:
Use identity:
\[
(a+b)^4 - (a-b)^4 = 8ab(a^2 + b^2)
\]
Step 1: Substitute \( a=\sqrt{3}, b=\sqrt{2} \).
\[ = 8(\sqrt{6})(3+2) = 8\sqrt{6} \cdot 5 = 40\sqrt{6} \]
Step 1: Substitute \( a=\sqrt{3}, b=\sqrt{2} \).
\[ = 8(\sqrt{6})(3+2) = 8\sqrt{6} \cdot 5 = 40\sqrt{6} \]
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