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What is the simplified form of ( (x-y)^2-x^2-y^2 )?( (x-y)^2-x^2-y^2 ) का सरल रूप क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(-2xy\)\(-2xy\)
Using the identity \((x-y)^2=x^2-2xy+y^2\), the expression becomes \(x^2-2xy+y^2-x^2-y^2\). The \(x^2\) and \(y^2\) terms cancel, leaving \(-2xy\). The result \(2xy\) would arise from \((x+y)^2\), not \((x-y)^2\). Exam tip: the middle term in \((a-b)^2\) is always negative, \(-2ab\).पहचान \((x-y)^2=x^2-2xy+y^2\) लगाने पर व्यंजक \(x^2-2xy+y^2-x^2-y^2\) बनता है। इसमें \(x^2\) और \(y^2\) के पद कट जाते हैं, इसलिए केवल \(-2xy\) बचता है। \(2xy\) तब मिलता यदि \((x+y)^2\) होता। परीक्षा टिप: \((a-b)^2\) में मध्य पद हमेशा ऋणात्मक \(-2ab\) होता है।
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