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Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials2 Marks
Question
Write the cube in expanded form : $\left(x-\frac{2}{3} y\right)^{3}$
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Answer

$\left(x-\frac{2}{3} y\right)^3=x^3-\left(\frac{2}{3} y\right)^3-3(x)\left(\frac{2}{3} y\right)\left(x-\frac{2}{3} y\right)$
(Using Identity $(a-b)^3=a^3-b^3-3 a b(a-b)$ )
$=x^3-\frac{8}{27} y^3-2 x y\left(x-\frac{2}{3} y\right)=x^3-\frac{8}{27} y^3-2 x^2 y+\frac{4}{3} x y^2$
$=x^3-2 x^2 y+\frac{4}{3} x y^2-\frac{8}{27} y^3$

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