分解因式:16(6x-1)(2x-1)(3x+1)(x-1)+25

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分解因式:16(6x-1)(2x-1)(3x+1)(x-1)+25
分解因式:16(6x-1)(2x-1)(3x+1)(x-1)+25

分解因式:16(6x-1)(2x-1)(3x+1)(x-1)+25
原式=(6x-1)[2(2x-1)][2(3x+1)][4(x-1)]+25
=[(6x-1)(4x-2)][(6x+2)(4x-4)]+25
=[(24x²-16x)+2](24x²-16x)-8]+25
=(24x²-16x)²-6(24x²-16x)-16+25
=(24x²-16x)²-6(24x²-16x)+9
=(24x²-16x-3)²

16(6x-1)(2x-1)(3x+1)(x-1)+25
=(6x-1)(4x-2)(6x+2)(4x-4)+25
=(24x^2-16x+2) (24x^2-16x-8)+25

设 24x^2-16x+2=t,

则原式=t(t-10)+25=(t-5)2=(24x^2-16x-3)^2