因式分解:(x2+2x+4)(x2+2x-3)-8

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因式分解:(x2+2x+4)(x2+2x-3)-8

(x^2+2x+4)(x^2+2x-3)-8
设m=x^2+2x+4
原式
=m(m-7)-8
=m^2-7m-8
=(m+1)(m-8)
=(x^2+2x+4+1)(x^2+2x+4-8)
=(x^2+2x+5)(x^2+2x-4)

(x2+2x+4)(x2+2x-3)-8=(x2+2x-3)(x2+2x-3)+7(x2+2x-3)-8
=(x2+2x-3+8)(x2+2x-3-1)
=(x2+2x+5)(x2+2x-4)