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x^2+x+2y-4y^2 因式分解

分类: 作业答案 • 2021-12-19 17:22:49
问题描述：

x^2+x+2y-4y^2 因式分解

答

x^2+x+2y-4y^2
=(x^2+x+1/4)-(4y^2 -2y+1/4)
=(x+1/2)^2-(2y-1/2)^2
=(x+1/2+2y-1/2)(x+1/2-2y+1/2)
=(x+2y)(x-2y+1)

答

原式=(x^2+x)-(4y^2-2y)
=(x^2+x+1/4-1/4)-(4y^2-2y+1/4-1/4)
=[(x+1/2)^2-1/4]-[(2y-1/2)^2-1/4]
=(x+1/2)^2-1/4-(2y-1/2)^2+1/4
=(x+1/2)^2-(2y-1/2)^2
=(x+1/2+2y-1/2)(x+1/2-2y+1/2)
=(x+2y)(x-2y+1)

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