(a-b)(3a+b)^2+(a+3b)^2(b-a)因式分解要过程

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(a-b)(3a+b)^2+(a+3b)^2(b-a)因式分解要过程

(a-b)(3a+b)^2+(a+3b)^2(b-a)因式分解要过程
(a-b)(3a+b)^2+(a+3b)^2(b-a)因式分解要过程

(a-b)(3a+b)^2+(a+3b)^2(b-a)因式分解要过程
(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)(3a+b-a-3b)(3a+b+a+3b)
=(a-b)(2a-2b)(4a+4b)
=8(a-b)(a-b)(a+b)
=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)(8a^2-8b^2)
8(a-b)(a^2-b^2)
8(a-b)(a+b)(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)(4a+4b)(2a+4b)
=8(a-b)(a+b)(a+2b)

(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)