分解因式 1)(x²+4x+8)²+3x(x²+4x+8)+2x²2) (2x²-3x+1)²-22x²+33x-13)

1个回答

  • 1)(x²+4x+8)²+3x(x²+4x+8)+2x²

    =(x²+4x+8+x)(x²+4x+8+2x) (把x²+4x+8看做一个整体)

    =(x²+5x+8)(x²+6x+8)

    =(x²+5x+8)(x+2)(x+4)

    2) (2x²-3x+1)²-22x²+33x-1

    =(2x²-3x+1)²-11(2x²-3x+1)+10

    =(2x²-3x+1-1)(2x²-3x+1-10) (这一步和第一题一样)

    =(2x²-3x)(2x²-3x-9)

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

    3) (6x-1)(2x-1)(3x-1)(x-1)+x²

    =(6x-1)(x-1)(2x-1)(3x-1)+x²

    =(6x²+1-7x)(6x²+1-5x)+x²

    =(6x²+1)²-12(6x²+1)x+35x²+x²

    =(6x²+1)²-12(6x²+1)x+36x²

    =[(6x²+1)-6x]²

    =(6x²-6x+1)²

    4) ab(a+b)²-(a+b)²+1

    =(ab-1)(a+b)²+1

    =(ab-1)a²+(ab-1)b²+2ab(ab-1)+1

    =(ab-1)a²+(ab-1)b²+2(ab)²-2ab+1

    =(ab-1)a²+(ab-1)b²+(ab)²+(ab)²-2ab+1

    =(ab-1)a²+(ab-1)b²+(ab)²+(ab²-2ab+1)

    =(ab-1)a²+(ab-1)b²+(ab)²+(ab-1)²

    =[(ab-1)a²+(ab)²]+[(ab-1)b²+(ab-1)²]

    =a²[(ab-1)+b²]+(ab-1)*[(ab-1)+b²]

    =(a²+ab-1)(b²+ab-1)

    5) x²+xy-6y²+x+13y-6

    =(x+3y)(x-2y)+(x+13y)-6 (这是关于x+3y和x-2y的式子)

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