(x2-5)2+8(x2-5)+16怎么因式分解

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(x2-5)2+8(x2-5)+16怎么因式分解
(x2-5)2+8(x2-5)+16怎么因式分解

(x2-5)2+8(x2-5)+16怎么因式分解
(x²-5)²+8(x²-5)+16
设 x²-5=m
原式=m²+8m+4²
=(m+4)²
=(x²-1)²
=[(x-1)(x+1)]²
=(x-1)²(x+1)²

(x²-5)²+8(x²-5)+16
=(x²-5+4)²
=(x²-1)²
=(x+1)²(x-1)²

(x²-5)²+8(x²-5)+16
=(x²-5+4)²
=(x²-1)²
=(x+1)²(x-1)²