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Factorization Of Algebraic Expressions [NEW] — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions [NEW]2 Marks
Question
Factorize the following expressions:
x3 - 8y3 + 27z3 + 18xyz
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Answer

x3 - 8y3 + 27z3 + 18xyz
= x3 + (-2y)3 + (3z)3 - 3 × x ×(-2y)(3z)
= (x + (-2y) + 3z)(x2 + (-2y)2 +(3z)2 - x(-2y) - (-2y)(3z) - 3z(x))
$\big[\because$ a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)$\big]$
= (x - 2y + 3z)(x2 + 4y2 + 9z2 + 2xy + 6yz - 3zx)
$\therefore$ x3 - 8y3 + 27z3 + 18xyz = (x - 2y + 3z)(x2 + 4y2 + 9z2 + 2xy + 6yz - 3zx)

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