Factorise : 27x^3 + y^3 + z^3 - 9xyz. - Vidyadip

Question

Factorise : $27x^3 + y^3 + z^3 - 9xyz.$

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Answer

$27x^3 + y^3 + z^3 - 9xyz.$
$(3x)^3 + (y)^3 + (z)^3 - 3(3x)(y)(z)$
$= (3x + y + z){(3x)^2 + (y)^2 + (z)^2 - (3x)(y) - (y)(z) - (z)(3x)}$
$($Using Identity $a^3+ b^3+ c^3– 3abc= (a + b + c)(a^2+ b^2+ c^2– ab – bc – ca))$
$= (3x + y + z)(9x^2 + y^2 + z^2 - 3xy - yz - 3zx).$

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