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Polynomials — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsPolynomials2 Marks
Question
Expand the following:
$(3 a-2 b)^3$
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Answer

$(3 a-2 b)^3=(3 a)^3+(-2 b)^3+3(3 a)(-2 b)(3 a-2 b)$
${\left[\text { Using identity, }(a-b)^3=a^3-b^3+3 a(-b)(a-b)\right]}$
$=27 a^3-8 b^3-18 a b(3 a-2 b)$
$=27 a^3-8 b^3-54 a^2 b+36 a b^2$
$=27 a^3-54 a^2 b+36 a b^2-8 b^3$

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