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几道因式分解～帮下忙～..(x+y)^2-2(X^2-Y^2)+(x-y)^2 (X^2-7X+6)(X^2-X-6)+56 -A^3+5A^2B+24AB^2

分类: 作业答案 • 2022-08-17 10:47:36
问题描述：

几道因式分解～帮下忙～
..(x+y)^2-2(X^2-Y^2)+(x-y)^2
(X^2-7X+6)(X^2-X-6)+56
-A^3+5A^2B+24AB^2

答

(x+y)^2-2(X^2-Y^2)+(x-y)^2
=(x+y)^2-2[(x+y)(x-y)]+(x-y)^2
=[(x+y)-(x-y)]^2
=4y^2
(X^2-7X+6)(X^2-X-6)+56
=(x-1)(x-6)(x+2)(x-3)+56
=(x^2-4x+3)(x^2-4x-12)+56
=(x^2-4x+3)^2-15(x^2-4x+3)+56
=(x^2-4x+3-8)(x^2-4x+3-7)
=(x^2-4x-5)(x^2-4x-4)
=(x-5)(x+1)(x^2-4x-4)
-A^3+5A^2B+24AB^2
=-A(A^2-5AB-24B^2)
=-A(A-8B)(A+3B)

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