Gujarat BoardEnglish MediumSTD 9MathsPolynomials2 Marks
Question
Factorise : $8 x^3+y^3+27 z^3-18 x y z$
✓
Answer
Here, we have
$8 x^3+y^3+27 z^3-18 x y z$
$=(2 x)^3+y^3+(3 z)^3-3(2 x)(y)(3 z)$
$=(2 x+y+3 z)\left[(2 x)^2+y^2+(3 z)^2-(2 x)(y)-(y)(3 z)-(2 x)(3 z)\right]$
$=(2 x+y+3 z)\left(4 x^2+y^2+9 z^2-2 x y-3 y z-6 x z\right)$
This is the required factorisation.
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