Question
Factorise : $8x^3 + y^3 + 27z^3 – 18xyz$
✓
Answer
Here, we have
$8x^3 + y^3 + 27z^3 - 18xyz$
$= (2x)^3 + y^3 + (3z)^3 – 3(2x)(y)(3z)$
$= (2x + y + 3z)[(2x)^2 + y^2 + (3z)^2 – (2x)(y) – (y)(3z) – (2x)(3z)]$
$= (2x + y + 3z) (4x^2 + y^2 + 9z^2 - 2xy - 3yz - 6xz)$
This is the required factorisation.
$8x^3 + y^3 + 27z^3 - 18xyz$
$= (2x)^3 + y^3 + (3z)^3 – 3(2x)(y)(3z)$
$= (2x + y + 3z)[(2x)^2 + y^2 + (3z)^2 – (2x)(y) – (y)(3z) – (2x)(3z)]$
$= (2x + y + 3z) (4x^2 + y^2 + 9z^2 - 2xy - 3yz - 6xz)$
This is the required factorisation.
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