因式分解:(x^2-7x+6)(x^2-x-6)+56
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(x^2-7x+6)(x^2-x-6)+56
=(x-1)(x-6)(x-3)(x+2)+56
=[(x-1)(x-3)][(x-6)(x+2)]+56
=(x^2-4x+3)(x^2-4x-12)+56
=(x^2-4x)^2-9(x^2-4x)-36+56
=(x^2-4x)^2-9(x^2-4x)+20
=(x^2-4x-4)(x^2-4x-5)
=(x+1)(x-5)(x^2-4x-4)
=(x-1)(x-6)(x-3)(x+2)+56
=[(x-1)(x-3)][(x-6)(x+2)]+56
=(x^2-4x+3)(x^2-4x-12)+56
=(x^2-4x)^2-9(x^2-4x)-36+56
=(x^2-4x)^2-9(x^2-4x)+20
=(x^2-4x-4)(x^2-4x-5)
=(x+1)(x-5)(x^2-4x-4)
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