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  • 將下列各式分解因式:(1) (m+n)²+n² (2)49(a-b)²-16(a+b)²

    將下列各式分解因式:(1) (m+n)²+n² (2)49(a-b)²-16(a+b)²
    將下列各式分解因式:(1) (m+n)²+n² (2)49(a-b)²-16(a+b)² (3) (2x+y)²-(x+2y)² (4) (x²+y²)²-x²y² (5) 3ax²-(3ay ^4) (6) p^4-1
    數(shù)學(xué)人氣:910 ℃時(shí)間:2020-05-09 03:51:59
    優(yōu)質(zhì)解答
    (1) (m+n)²-n²
    =(m+n+n)(m+n-n)
    =m(m+2n)
    (2)49(a-b)²-16(a+b)²
    =[7(a-b)+4(a+b)][7(a-b)-4(a+b)]
    =(11a-3b)(3a-11b)
    (3) (2x+y)²-(x+2y)²
    =(2x+y+x+2y)(2x+y-x-2y)
    =3(x+y)(x-y)
    (4) (x²+y²)²-x²y²
    =(x²+y²+xy)(x²+y²-xy)
    (5) 3ax²-(3ay ^4)
    =3a(x²-y^4)
    =3a(x+y²)(x-y²)
    (6) p^4-1
    =(p²+1)(p²-1)
    =(p²+1)(p+1)(p-1)
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