因式分解因式分解：(x²-7x+6)(x²-x-6)+56

(x²-7x+6)(x²-x-6)+56
=(x-1)(x-6)(x-3)(x+2)+56
=(x-1)(x-3)(x-6)(x+2)+56
=(x²-4x+3)(x²-4x-12)+56
=(x²-4x)²-9(x²-4x)-36+56
=(x²-4x)²-9(x²-4x)+20
=(x²-4x-4)(x²-4x-5)
=(x²-4x-4)(x-5)(x+1)
=(x-5)(x+1)(x²-4x-4)

(x²-7x+6)(x²-x-6)+56
=(x-1)(x-6)(x-3)(x+2)+56

你好!
原式= [(x²-4x) - (3x-6)] [(x²-4x)+(3x-6)] +56
=(x²-4x)²-(3x+6)² +56 【平方差公式】
=(x²-4x)² - 9x²-36x-36+56
= (x²-4x)² - 9(x²+4x) +20
=(x²-4x-4)(x²-4x-5) 【将(x²-4x)看作一个整体,用十字相乘法】
= (x²-4x-4)(x+1)(x-5)

原式=x^4-x^3-6x^2-7x^3+7x^2+42x+6x^2-6x-36+56
=x^4-8x^3+7x^2+36x+20
=(x^2-4x-4)(x^2-4x-5)