16(6x-1)(2x-1)(3x+1)(x-1)+25分解因式

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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分解因式

16(6x-1)(2x-1)(3x+1)(x-1)+25分解因式
解】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

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=Y,
原式=Y(Y-10)+25=(Y-5)^2=(24x^2-16x-3)^2

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