(a-b)(3a+b)^2+(a+3b)^2(b-a)详细解

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(a-b)(3a+b)^2+(a+3b)^2(b-a)详细解
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(a-b)(3a+b)^2+(a+3b)^2(b-a)详细解
(a-b)(3a+b)^2+(a+3b)^2(b-a)详细解

(a-b)(3a+b)^2+(a+3b)^2(b-a)详细解
(a-b)(3a+b)^2+(a+3b)^2(b-a)
=(a-b)[(3a+b)²-(a+3b)²]
=(a-b)(3a+b+a+3b)(3a+b-a-3b)
=(a-b)(4a+4b)(2a-2b)
=8(a-b)²(a+b)

(a-b)(3a+b)^2+(a+3b)^2(b-a)
=(a-b)(3a+b)^2-(a+3b)^2(a-b)
=(a-b)【(3a+b)²-(a+3b)²】
=(a-b)(3a+b-a-3b)(3a+b+a+3b)
=(a-b)×(2a-2b)×(4a+4b)
=8(a+b)(a-b)²

(3a+b)²((a-b)+(b-a))
=(3a+b)²*0
=0