因式分解 (a-1)(a+1)(a+3)(a+5)+16

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因式分解 (a-1)(a+1)(a+3)(a+5)+16
因式分解 (a-1)(a+1)(a+3)(a+5)+16

因式分解 (a-1)(a+1)(a+3)(a+5)+16
(a-1)(a+1)(a+3)(a+5)+16
=[(a-1)(a+5)][(a+1)(a+3)]+16
=(a^2+4a-5)(a^2+4a+3)+16
=(a^2+4a)^2-2(a^2+4a)-15+16
=(a^2+4a-1)^2
=(a-√5+2)^2(a+√5+2)^2

(a-1)(a+1)(a+3)(a+5)+16
=[(a-1)(a+5)][(a+1)(a+3)]+16
=(a^2+4a-5)(a^2+4a+3)+16
设a^2+4a-5为b
=b(b+8)+16
=b^2+8b+16
十字相乘
=(b+4)^2
=(a^2+4a-1)^2

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