Factorization Of Algebraic Expressions — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions2 Marks
Question
Factorize the following expressions: $27 x^3-y^3-z^3-9 x y z$
✓
Answer
We know that
$x^3+y^3+z^3-3 x y z=(x+y+z)\left(x^2+y^2+z^2-x y-y z-z x\right)$
$\therefore 27 x^3-y^3-z^3-9 x y z$
$=(3 x)^3+(-y)^3+(-z)^3-3(3 x)(-y)(-z)$
$=[3 x+(-y)+(-z)]\left[(3 x)^2+(-y)^2+(-z)^2-(3 x)(-y)(-z)-(-z)(3 x)\right]$
$=(3 x-y-z)\left(9 x^2+y^2+z^2+3 x y-y z+3 z x\right)$
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