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Factorization Of Algebraic Expressions — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSFactorization Of Algebraic Expressions2 Marks
Question
Factorize the following expressions: $x^3 - 8y^3 + 27z^3 + 18xyz$
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Answer

$x^3 - 8y^3 + 27z^3 + 18xyz$
$= x^3 + (-2y)^3 + (3z)3 - 3 \times x \times (-2y)(3z)$
$= (x + (-2y) + 3z)(x^2 + (-2y)^2 +(3z)^2 - x(-2y) - (-2y)(3z) - 3z(x))$
$\big[\because a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - bc - ca)\big]$
$= (x - 2y + 3z)(x^2 + 4y^2+ 9z^2 + 2xy + 6yz - 3zx)$
$\therefore x^3 - 8y^3 + 27z^3 + 18xyz$
$ = (x - 2y + 3z)(x^2 + 4y^2 + 9z^2 + 2xy + 6yz - 3zx)$

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