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Find a common factor in the given algebraic expressions: m(x-y)-n(y-x)

Mathematics

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Answer

x-y

Step-by-step solution

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यहाँ दिइएका बीजगणितीय अभिव्यक्तिहरूमा साझा गुणनखण्ड पत्ता लगाउनुपर्नेछ।

अभिव्यक्तिहरू हुन्:

  1. m(x−y)m(x-y)
  2. n(y−x)n(y-x)
  1. दिएका अभिव्यक्तिहरूलाई लेख्नुहोस्।

    पहिलो अभिव्यक्ति: m(x−y)m(x-y)
    दोस्रो अभिव्यक्ति: n(y−x)n(y-x)

  2. दोस्रो अभिव्यक्तिलाई पुन

    लेख्नुहोस् ताकि साझा गुणनखण्ड स्पष्ट होस्।
    हामीलाई थाहा छ कि y−x=−(x−y)y-x = -(x-y)।
    त्यसैले, दोस्रो अभिव्यक्तिलाई यसरी लेख्न सकिन्छ:

    n(y−x)=n(−(x−y))=−n(x−y)n(y-x) = n(-(x-y)) = -n(x-y)
  3. अब दुवै अभिव्यक्तिमा साझा गुणनखण्ड पत्ता लगाउनुहोस्।

    पहिलो अभिव्यक्ति: m(x−y)m(x-y)
    दोस्रो अभिव्यक्ति: −n(x−y)-n(x-y)
    दुवै अभिव्यक्तिमा (x−y)(x-y) साझा गुणनखण्ड हो।

    अन्तिम उत्तर हो:

    x−yx-y
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