一道数学因式分解,用换元法
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一道数学因式分解,用换元法
(6x-1)(2x-1)(3x-1)(x-1)+x^2
(6x-1)(2x-1)(3x-1)(x-1)+x^2
(6x-1)(2x-1)(3x-1)(x-1)+x^2
=[(6x-1)(x-1)][(2x-1)(3x-1)]+x^2
=(6x^2-7x+1)(6x^2-5x+1)+x^2
设A=6x^2+1
原式=(A-7x)(A-5x)+x^2
=A^2-12Ax+36x^2
=(A-6x)^2
=(6x^2-6x+1)^2
=[(6x-1)(x-1)][(2x-1)(3x-1)]+x^2
=(6x^2-7x+1)(6x^2-5x+1)+x^2
设A=6x^2+1
原式=(A-7x)(A-5x)+x^2
=A^2-12Ax+36x^2
=(A-6x)^2
=(6x^2-6x+1)^2