Factorisation of Polynomials — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsFactorisation of Polynomials2 Marks
Question
Factorise: $8\text{x}^3-\frac{1}{27\text{y}^3}$
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Answer
We know that: Since a3 - b3 = (a - b)(a2 + a × b + b2) Let us rewrite $8\text{x}^3-\frac{1}{27\text{y}^3}$ $=(2\text{x})^3-\Big(\frac{1}{3\text{y}}\Big)^3$ $=\Big(2\text{x}-\frac{1}{3\text{y}}\Big)\bigg[(2\text{x})^2+2\text{x}\times\frac{1}{3\text{y}}+\Big(\frac{1}{3\text{y}}\Big)^2\bigg]$ $=\Big(2\text{x}-\frac{1}{3\text{y}}\Big)\Big(4\text{x}^2+\frac{2\text{x}}{3\text{y}}+\frac{1}{9\text{y}^2}\Big)$
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