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For two algebraic expressions \(U\) and \(V\), which part remains unchanged in the expansions of \((U+V)^2\) and \((U-V)^2\)?दो बीजीय व्यंजकों \(U\) और \(V\) के लिए, \((U+V)^2\) तथा \((U-V)^2\) के प्रसारों में कौन-सा भाग अपरिवर्तित रहता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(U^2+V^2\)\(U^2+V^2\)
Since \((U+V)^2=U^2+2UV+V^2\) and \((U-V)^2=U^2-2UV+V^2\), \(U^2+V^2\) remains unchanged. Only the middle term changes sign. Exam tip: compare the outer terms first.\((U+V)^2=U^2+2UV+V^2\) और \((U-V)^2=U^2-2UV+V^2\) हैं। इसलिए \(U^2+V^2\) समान रहता है; केवल मध्य पद का चिह्न बदलता है। परीक्षा में बाहरी पद पहले मिलाएँ।
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