Factorise : 8 x^{3}+y^{3}-27 z^{3}+18 x y z | vedclass

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(D) The given expression is $8 x^{3}+y^{3}-27 z^{3}+18 x y z$.We use the algebraic identity: $a^{3}+b^{3}+c^{3}-3 a b c = (a+b+c)(a^{2}+b^{2}+c^{2}-a

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(D) The given expression is $8 x^{3}+y^{3}-27 z^{3}+18 x y z$.
We use the algebraic identity: $a^{3}+b^{3}+c^{3}-3 a b c = (a+b+c)(a^{2}+b^{2}+c^{2}-a b-b c-c a)$.
Rewrite the expression as: $(2 x)^{3}+(y)^{3}+(-3 z)^{3}-3(2 x)(y)(-3 z)$.
Here,$a = 2 x$,$b = y$,and $c = -3 z$.
Applying the identity:
$= (2 x+y-3 z)((2 x)^{2}+(y)^{2}+(-3 z)^{2}-(2 x)(y)-(y)(-3 z)-(-3 z)(2 x))$.
Simplifying the terms:
$= (2 x+y-3 z)(4 x^{2}+y^{2}+9 z^{2}-2 x y+3 y z+6 z x)$.

Factorise $: 8 x^{3}+y^{3}-27 z^{3}+18 x y z$

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