Factorize 3 -3 a3 - b3 - 5 -5c3 -3 -15 abc

3 √(3) a^3 b^3 5 √(5)c^3 3 √(15) abc ⇒ ( √(3)a )^3 + ( b)^3 + ( √(5)c)^3 3 √(3)a × ( b ) × ( √(5)c) = (√(3)a b √(5)c) [ ( √(3)a)^2 + ( b)^2+ ( √(5) ...

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Byju's Answer

Standard VIII

Mathematics

Factorisation Using Algebraic Identities

Factorize 3 √...

Question

Factorize $3 \sqrt{3} a^{3} - b^{3} - 5 \sqrt{5} c^{3} - 3 \sqrt{15} a b c$

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Solution

$3 \sqrt{3} a^{3} - b^{3} - 5 \sqrt{5} c^{3} - 3 \sqrt{15} a b c \Rightarrow (\sqrt{3} a)^{3} + (- b)^{3} + (- \sqrt{5} c)^{3} - 3 \sqrt{3} a \times (- b) \times (- \sqrt{5} c) = (\sqrt{3} a - b - \sqrt{5} c) [(\sqrt{3} a)^{2} + (- b)^{2} + (- \sqrt{5} c)^{2} - \sqrt{3} a \times (- b) - (- b) (- \sqrt{5} c) - (- \sqrt{5} c) \times \sqrt{3} a] = (\sqrt{3} a - b - \sqrt{5} c) (3 a^{2} + b^{2} + 5 c^{2} + \sqrt{3} a b - \sqrt{5} b c + \sqrt{15} c a)$

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Factorize 3√3a3−b3−5√5c3−3√15abc

3√3a3−b3−5√5c3−3√15abc⇒(√3a)3+(−b)3+(−√5c)3−3√3a×(−b)×(−√5c)=(√3a−b−√5c)[(√3a)2+(−b)2+(−√5c)2−√3a×(−b)−(−b)(−√5c)−(−√5c)×√3a]=(√3a−b−√5c)(3a2+b2+5c2+√3ab−√5bc+√15ca)

Factorize $3 \sqrt{3} a^{3} - b^{3} - 5 \sqrt{5} c^{3} - 3 \sqrt{15} a b c$