因式分解:X³+9X²+26X+24,bc(b+c)+ca(c-a)-ab(a+b),8x&sup3

1个回答

  • X³+9X²+26X+24

    =(X³+7X²+12X)+(2X²+14X+24)

    =X(X²+7X+12)+2(X²+7X+12)

    =(X+2)(X²+7X+12)

    =(X+2)(X+3)(X+4)

    bc(b+c)+ca(c-a)-ab(a+b)

    =c[b(b+c)+a(c-a)]-ab(a+b)

    =c(b²+bc+ac-a²)-ab(a+b)

    =c[(bc+ac)+(b²-a²)]-ab(a+b)

    =c[c(b+a)+(b+a)(b-a)]-ab(a+b)

    =c(a+b)(c+b-a)-ab(a+b)

    =(a+b)(c²+bc-ac-ab)

    =(a+b)(b+c)(c-a)

    8x³-(x-y)³-(x+y)³

    =8x³-[(x-y)³+(x+y)³]

    =8x³-[(x-y)+(x+y)]*[(x-y)²+(x+y)²-(x-y)(x+y)]

    =8x³-2x*[2x²+2y²-(x²-y²)]

    =8x³-2x(x²+3y²)

    =8x³-2x³-6xy²

    =6x³-6xy²

    =6x(x²-y²)

    =6x(x-y)(x+y)