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Which is the correct factorisation of (2x^2+5xy-12y^2)?(2x^2+5xy-12y^2) का सही गुणनखंड कौन सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \((2x-3y)(x+4y)\)\((2x-3y)(x+4y)\)
Split the middle term as \(5xy=8xy-3xy\), since \(8\times(-3)=-24=2\times(-12)\). Thus, \(2x^2+5xy-12y^2=2x^2+8xy-3xy-12y^2\), which factors by grouping to \((2x-3y)(x+4y)\). Option B gives a middle term of \(-5xy\). Exam tip: expand the factors briefly to check both the middle term and the constant term.मध्य पद को \(5xy=8xy-3xy\) के रूप में लिखें, क्योंकि \(8\times(-3)=-24=2\times(-12)\)। तब \(2x^2+5xy-12y^2=2x^2+8xy-3xy-12y^2\) और समूह बनाने पर \((2x-3y)(x+4y)\) मिलता है। विकल्प B में मध्य पद \(-5xy\) बनता है। परीक्षा टिप: गुणनखंडों का विस्तार करके मध्य पद और अंतिम पद दोनों अवश्य जाँचें।
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