邓伦李沁快乐大本营:分解因式:(x-1)(x-2)(x-3)(x-4)-48

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(x-1)(x-2)(x-3)(x-4)-48
=(x-1)(x-4)(x-2)(x-3)-48
=(x^2-5x+4)(x^2-5x+6)-48
=(x^2-5x)^2+10(x^2-5x+6)-24
=(x^2-5x-2)(x^2-5x+12)

解:
(x-1)(x-2)(x-3)(x-4)-48
=(x-1)(x-4)(x-2)(x-3)-48
=(x^2-5x+4)(x^2-5x+6)-48
=(x^2-5x)^2+10(x^2-5x+6)-24
=(x^2-5x-2)(x^2-5x+12)
(^表示平方)

(x-1)(x-2)(x-3)(x-4)-48
=(x-1)(x-4)(x-2)(x-3)-48
=(x^2-5x+4)(x^2-5x+6)-48
=(x^2-5x)^2+10(x^2-5x+6)-24
=(x^2-5x-2)(x^2-5x+12)
(^表示平方)

(x-1)(x-2)(x-3)(x-4)-48
=(x-1)(x-4)(x-2)(x-3)-48
=(x^2-5x+4)(x^2-5x+6)-48
=(x^2-5x+4)^2+2(x^2-5x+4)-48
=(x^2-5x+4-6)(x^2-5x+4+8)
==(x^2-5x-2)(x^2-5x+12)

(x-1)(x-2)(x-3)(x-4)-48
=(x-1)(x-4)(x-2)(x-3)-48
=(x^2-5x+4)(x^2-5x+6)-48
=(x^2-5x+4)^2+2(x^2-5x+4)-48
=(x^2-5x+4-6)(x^2-5x+4+8)
==(x^2-5x-2)(x^2-5x+12)