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What is the coefficient of the term containing \(a^2b\) in \((3a-b)^3\)?\((3a-b)^3\) में \(a^2b\) वाले पद का गुणांक क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(-27\)\(-27\)
Expand using \((x-y)^3=x^3-3x^2y+3xy^2-y^3\). Let \(x=3a\) and \(y=b\). Then the \(a^2b\) term comes from \(-3x^2y=-3(3a)^2(b)=-3\cdot 9a^2b=-27a^2b\). So the coefficient of \(a^2b\) is \(-27\).\((x-y)^3=x^3-3x^2y+3xy^2-y^3\) का प्रयोग करके विस्तार करें। यहाँ \(x=3a\) और \(y=b\) लें। \(a^2b\) वाला पद \(-3x^2y\) से आएगा:
\(-3x^2y=-3(3a)^2(b)=-3\cdot 9a^2b=-27a^2b\)। अतः \(a^2b\) का गुणांक \(-27\) है।
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