2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²因式分解

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2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²因式分解

2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²因式分解
2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²因式分解

2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²因式分解
本题的解题思路,可以这样进行思考:设x²+1=a,x²+6x+1=b
则原式=2b²+5ab+2a²=(b+2a)(2b+1)
把x²+1=a,x²+6x+1=b代入上式得:
=(x²+6x+1+2x²+2)(2x²+12x+3)
=3(x²+2x+1)(2x²+12x+3)
=3(x+1)²(2x²+12x+3)
当然,你可以不用设,而直接采取十字相乘法.这题利用了整体思想.

2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²
=[2(x²+6x+1)+(x²+1)][(x²+6x+1)+2(x²+1)]
=(3x^2+12x+2)(3x^2+6x+2)

2(x²+6x+1)²+5(x²+1)(x²+6x+1)+2(x²+1)²=<2(x²+6x+1)+(x²+1)><(x²+6x+1)+2(x²+1)>=3(x²+4x+1)(3x²+6x+2)
把(x²+6x+1)设作a,把(x²+1)设作b,因式分解后,再带入合并同类项即可。

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