数学因式分解题(用平方差公式)!

1个回答

  • ①x²-(y-1)²

    =(x+y-1)(x-y+1)

    ②-1+(m-1)²

    =(m-1+1)(m-1-1)

    =m(m-2)

    ③(2x+y)²-(2x-3y)²

    =(2x+y+2x-3y)(2x+y-2x+3y)

    =4y(4x-2y)

    ④25(x-y)²-(x+y)²

    =(5(x-y)+x+y)(5(x-y)-x-y)

    =(6x-4y)(4x-6y)

    ⑤9(m+n)²-4(2m-n)²

    =(3(m+n)+2(2m-n))(3(m+n)-2(2m-n))

    =(3m+3n+4m-2n)(3m+3n-4m+2n)

    =(7m+n)(5n-m)

    ⑥(x-y+z)²-(x-y-z)²

    =(x-y+z+x-y-z)(x-y+z-x+y+z)

    =2z(2x-2y)

    =4z(x-y)

    ⑦198²-202²

    =(200-2)²-(200+2)²

    =(200-2+200+2)(200-2-200-2)

    =400×(-4)

    =-1600