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What is the simplified form of \( (x-1)(x+1)(x^2+1) \)?\( (x-1)(x+1)(x^2+1) \) का सरल रूप क्या है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x^4-1\)\(x^4-1\)
First, use the identity \((x-1)(x+1)=x^2-1\). The expression then becomes \((x^2-1)(x^2+1)\), which again has the form \((a-b)(a+b)=a^2-b^2\). Therefore, it simplifies to \(x^4-1\). \(x^4+1\) is not the result of this difference-of-squares identity. Exam tip: identify conjugate binomial pairs and apply identities step by step.पहले सर्वसमिका \((x-1)(x+1)=x^2-1\) लगाएँ। अब व्यंजक \((x^2-1)(x^2+1)\) है, जो फिर से \((a-b)(a+b)=a^2-b^2\) के रूप में है। अतः इसका मान \(x^4-1\) होगा। \(x^4+1\) योग का सही परिणाम नहीं है। परीक्षा टिप: ऐसे प्रश्नों में पहले संयुग्म द्विपदों को पहचानकर क्रम से सर्वसमिका लगाएँ।
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