Simplify p²-2p9+9² P³-p9²+p²9-9³

Mathematics

ScanSolve AI Answer

Answer

p−q(p+q)2\frac{p-q}{(p+q)^2}

Step-by-step solution

4 steps

Huu hapa ni urahisishaji wa usemi:

  1. Rahisisha nambari.

    Nambari ni p2−2pq+q2p^2 - 2pq + q^2. Huu ni mraba kamili, ambao unaweza kuandikwa kama (p−q)2(p-q)^2.

  2. Rahisisha kigawe.

    Kigawe ni p3−pq2+p2q−q3p^3 - pq^2 + p^2q - q^3. Tunaweza kupanga upya na kutoa vigezo vya kawaida:

    p3+p2q−pq2−q3p^3 + p^2q - pq^2 - q^3

    Panga mafungu:

    (p3+p2q)−(pq2+q3)(p^3 + p^2q) - (pq^2 + q^3)

    Toa vigezo vya kawaida kutoka kila fungu:

    p2(p+q)−q2(p+q)p^2(p+q) - q^2(p+q)

    Toa (p+q)(p+q) kama kigezo cha kawaida:

    (p+q)(p2−q2)(p+q)(p^2 - q^2)

    Tumia tofauti ya fomula ya miraba, a2−b2=(a−b)(a+b)a^2 - b^2 = (a-b)(a+b), kwa p2−q2p^2 - q^2:

    (p+q)(p−q)(p+q)(p+q)(p-q)(p+q)

    Hii inaweza kuandikwa kama:

    (p+q)2(p−q)(p+q)^2(p-q)

  3. Badilisha fomu zilizorahisishwa kwenye usemi asilia.

    (p−q)2(p+q)2(p−q)\frac{(p-q)^2}{(p+q)^2(p-q)}

  4. Futa vigezo vya kawaida.

    Futa kigezo kimoja cha (p−q)(p-q) kutoka nambari na kigawe:

    p−q(p+q)2\frac{p-q}{(p+q)^2}
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