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A student factorised \(12m^2-7mn-10n^2\) as \((3m-2n)(4m+5n)\). Which is the correct factorisation after checking the sign of the middle term?एक विद्यार्थी ने \(12m^2-7mn-10n^2\) का गुणनखंडन \((3m-2n)(4m+5n)\) लिखा। मध्य पद के चिह्न की जाँच करने पर सही गुणनखंडन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \((3m+2n)(4m-5n)\)\((3m+2n)(4m-5n)\)
In \((3m+2n)(4m-5n)\), the cross-products are \(-15mn\) and \(+8mn\), giving \(-7mn\). Option B gives \(+7mn\), so its middle-term sign is wrong. Exam tip: always add the cross-products to verify factorisation.\((3m+2n)(4m-5n)\) में बाहरी और भीतरी गुणनफल \(-15mn\) तथा \(+8mn\) हैं, जिनका योग \(-7mn\) है। विकल्प B से \(+7mn\) मिलता है। परीक्षा में मध्य पद के चिह्न को अवश्य मिलाएँ।
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