Factorise:2 sqrt{2} a^{3} + 8 b^{3} - 27 c^{3 | vedclass

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Question

(A) We use the algebraic identity: $x^{3} + y^{3} + z^{3} - 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} - xy - yz - zx)$.Given expression: $2 \sqrt{2} a^

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$(\sqrt{2} a + 2 b - 3 c)(2 a^{2} + 4 b^{2} + 9 c^{2} - 2 \sqrt{2} a b + 6 b c + 3 \sqrt{2} c a)$

Vedclass · Answer

(A) We use the algebraic identity: $x^{3} + y^{3} + z^{3} - 3xyz = (x + y + z)(x^{2} + y^{2} + z^{2} - xy - yz - zx)$.Given expression: $2 \sqrt{2} a^{3} + 8 b^{3} - 27 c^{3} + 18 \sqrt{2} a b c$This can be rewritten as: $(\sqrt{2} a)^{3} + (2 b)^{3} + (-3 c)^{3} - 3(\sqrt{2} a)(2 b)(-3 c)$.Here,$x = \sqrt{2} a$,$y = 2 b$,and $z = -3 c$.Applying the identity:$= (\sqrt{2} a + 2 b - 3 c)((\sqrt{2} a)^{2} + (2 b)^{2} + (-3 c)^{2} - (\sqrt{2} a)(2 b) - (2 b)(-3 c) - (-3 c)(\sqrt{2} a))$$= (\sqrt{2} a + 2 b - 3 c)(2 a^{2} + 4 b^{2} + 9 c^{2} - 2 \sqrt{2} a b + 6 b c + 3 \sqrt{2} c a)$.

Factorise:
$2 \sqrt{2} a^{3} + 8 b^{3} - 27 c^{3} + 18 \sqrt{2} a b c$

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Factorise:$2 \sqrt{2} a^{3} + 8 b^{3} - 27 c^{3} + 18 \sqrt{2} a b c$