因式分解：(x+y)^3(x-y)-(x+y)(x-y)^3,9x^2-16(a+b)^2

来源：学生作业帮助网编辑：作业帮时间：2024/05/01 10:59:28

因式分解：(x+y)^3(x-y)-(x+y)(x-y)^3,9x^2-16(a+b)^2
因式分解：(x+y)^3(x-y)-(x+y)(x-y)^3,9x^2-16(a+b)^2

因式分解：(x+y)^3(x-y)-(x+y)(x-y)^3,9x^2-16(a+b)^2
(x+y)^3(x-y)-(x+y)(x-y)^3
=(x+y)(x-y)[(x+y)²-(x-y)²]
=(x+y)(x-y)(x+y+x-y)(x+y-x+y)
=4xy(x+y)(x-y)
9x^2-16(a+b)^2
=(3x)²-[4(a+b)]²
=(3x+4a+4b)(3x-4a-4b)

(1)=(x^2-y^2)*4xy
(2)=(3x-4a-ab)(3x+4a+4b)

(x+y)^3(x-y)-(x+y)(x-y)^3
=(x+y)(x-y) { (x+y)^2 -(x-y)^2}}
=(x+y)(x-y) { 4xy }
= 4xy(x+y)(x-y)
9x^2-16(a+b)^2
={3x+4(a+b)}{3x-4(a+b)}
=(3x+4a+4b)(3x-4a-4b)

(x+y)^3(x-y)-(x+y)(x-y)^3=(x+y)(x-y)[(x+y)²-(x-y)²]
=(x+y)(x-y)[(x+y)+(x-y)][(x+y)-(x-y)]
=(x+...

全部展开

(x+y)^3(x-y)-(x+y)(x-y)^3=(x+y)(x-y)[(x+y)²-(x-y)²]
=(x+y)(x-y)[(x+y)+(x-y)][(x+y)-(x-y)]
=(x+y)(x-y)(2x)(2y)
=4xy(x+y)(x-y)；
9x^2-16(a+b)^2=[3x+4(a+b)][3x-4(a+b)]
=(3x+4a+4b)(3x-4a-4b)。

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