Factorize 2 -2a3- 3 -3 b3 -c3 -3 -6 abc

2 √(2)a^3+ 3 √(3 )b^3 +c^3 3 √(6 ) abc = (√(2)a )^3 + ( √(3)b)^3 + (c)^3 3 ×√(2)a ×√(3)b × c = ( √(2) a + √(3)b + c ) [ (√(2)a)^2 + ( √(3)b)^2 + c^2 √(2 ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

Factorize 2 √...

Question

Factorize $2 \sqrt{2} a^{3} + 3 \sqrt{3} b^{3} + c^{3} - 3 \sqrt{6} a b c$

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Solution

$2 \sqrt{2} a^{3} + 3 \sqrt{3} b^{3} + c^{3} - 3 \sqrt{6} a b c = (\sqrt{2} a)^{3} + (\sqrt{3} b)^{3} + (c)^{3} - 3 \times \sqrt{2} a \times \sqrt{3} b \times c = (\sqrt{2} a + \sqrt{3} b + c) [(\sqrt{2} a)^{2} + (\sqrt{3} b)^{2} + c^{2} - \sqrt{2} a \times \sqrt{3} b - \sqrt{3} b \times c - c \times \sqrt{2} a] = (\sqrt{2} a + \sqrt{3} b + c) (2 a^{2} + 3 b^{2} + c^{2} - \sqrt{6} a b - \sqrt{3} b c - \sqrt{2} c a)$

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Factorize 2√2a3+3√3b3+c3−3√6abc

2√2a3+3√3b3+c3−3√6abc=(√2a)3+(√3b)3+(c)3−3×√2a×√3b×c=(√2a+√3b+c)[(√2a)2+(√3b)2+c2−√2a×√3b−√3b×c−c×√2a]=(√2a+√3b+c)(2a2+3b2+c2−√6ab−√3bc−√2ca)

Factorize $2 \sqrt{2} a^{3} + 3 \sqrt{3} b^{3} + c^{3} - 3 \sqrt{6} a b c$