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因式分解：a(x-y)^2+b(y-x)^3 4(x-y)^2+8(y-x)(x+y)1.a(x-y)^2+b(y-x)^3 2.4(x-y)^2+8(y-x)(x+y)

分类: 作业答案 • 2022-05-25 18:05:54
问题描述：

因式分解：a(x-y)^2+b(y-x)^3 4(x-y)^2+8(y-x)(x+y)
1.a(x-y)^2+b(y-x)^3
2.4(x-y)^2+8(y-x)(x+y)

答

a(x-y)^2+b(y-x)^3
=(y-x)^2(a+y-x)
4(x-y)^2+8(y-x)(x+y)
=4(x-y)(x-y-2x-2y)
=-4(x-y)(x+3y)

答

a(x-y)^2+b(y-x)^3
=a(x-y)^2-b(x-y)^3
=(x-y)^2[a-b(x-y)]
=(x-y)^2(a-bx+by)
4(x-y)^2+8(y-x)(x+y)
=4(x-y)^2-8(x-y)(x+y)
=4(x-y)[(x-y)-2(x+y)]
=4(x-y)(x-y-2x-2y)
=4(x-y)(-x-3y)
=-4(x-y)(x+3y)

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