(√(3)+√(2))^6 (√(3) √(2))^6 #160; #160; #160; #160; #160; a^3+b^3=(a+b)(a^2+b^2 ab) #160; #160; #160; #160; #160; #1 ...

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Expansion of (x^2 - y^2)

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Question

Evaluate: ${(\sqrt{3} + \sqrt{2})}^{6} - {(\sqrt{3} - \sqrt{2})}^{6}$

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Solution

$(\sqrt{3} + \sqrt{2})^{6} - (\sqrt{3} - \sqrt{2})^{6}$ $a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$
$a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)$
$((\sqrt{3} + \sqrt{2})^{3})^{2} - ((\sqrt{3} - \sqrt{2})^{3})^{2}$
$((\sqrt{3} + \sqrt{2})^{3} + (\sqrt{3} + \sqrt{2})^{3}) ((\sqrt{3} + \sqrt{2})^{3} - (\sqrt{3} - \sqrt{2})^{3})$
$(\sqrt{3} + \sqrt{2} + \sqrt{3} - \sqrt{2}) ((\sqrt{3} + \sqrt{2})^{2} + (\sqrt{3} - \sqrt{2})^{2} - (\sqrt{3} + \sqrt{2}) (\sqrt{3} - \sqrt{2})) ((\sqrt{3} + \sqrt{2} - (\sqrt{3} - \sqrt{2})) ((\sqrt{3} + \sqrt{2})^{2} + (\sqrt{3} - \sqrt{2})^{2} + (\sqrt{3} + \sqrt{2}) (\sqrt{3} - \sqrt{2}))$
$(2 \sqrt{3}) (3 + 2 + 2 \sqrt{3} + 3 + 2 - 2 \sqrt{3} - 3 + 2) (2 \sqrt{2}) (3 + 2 + 2 \sqrt{3} + 3 + 2 - 2 \sqrt{3} + 3 - 2)$
$(2 \sqrt{3}) (9) (2 \sqrt{2}) (11)$
$(4 \sqrt{6}) (99)$
$396 \sqrt{6}$ .

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