因式分解:(x2-2x)(x2-2x-3) (a2-5a+5)(a2-5a-3)-9 (a+1)(a+3)(a+5)(a
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因式分解:(x2-2x)(x2-2x-3) (a2-5a+5)(a2-5a-3)-9 (a+1)(a+3)(a+5)(a+7)+15
①原式=x(x-2)(x-3)(x+1)
②原式=(a²-5a)²+2(a²-5a)-24[将(a²-5a)看作整体展开]
=(a²-5a-4)(a²-5a+6)[将(a²-5a)看作整体分解因式]
=(a²-5a)(a-2)(a-3)[有理数范围]
=(a-5/2+√41/2)(a-5/2-√41/2)(a-2)(a-3)[实数范围]
③原式=[(a+1)(a+7)][(a+3)(a+5)]+15
=(a²+8a+7)(a²+8a+15)+15
=(a²+8a)²+22(a²+8a)+120[将(a²+8a)看作整体展开]
=(a²+8a+10)(a²+8a+12)[将(a²+8a)看作整体分解因式]
=(a²+8a+10)(a+2)(a+6)
=(a+4+√6)(a+4-√6)(a+2)(a+6)
②原式=(a²-5a)²+2(a²-5a)-24[将(a²-5a)看作整体展开]
=(a²-5a-4)(a²-5a+6)[将(a²-5a)看作整体分解因式]
=(a²-5a)(a-2)(a-3)[有理数范围]
=(a-5/2+√41/2)(a-5/2-√41/2)(a-2)(a-3)[实数范围]
③原式=[(a+1)(a+7)][(a+3)(a+5)]+15
=(a²+8a+7)(a²+8a+15)+15
=(a²+8a)²+22(a²+8a)+120[将(a²+8a)看作整体展开]
=(a²+8a+10)(a²+8a+12)[将(a²+8a)看作整体分解因式]
=(a²+8a+10)(a+2)(a+6)
=(a+4+√6)(a+4-√6)(a+2)(a+6)
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