Question

因式分解:（a-b）（3a+b）²+（a+3b）²（b–a）

Answer 1

(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)(4a+4b)(2a-2b)
=8(a-b)²(a+b)

Answer 2

（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)(2a-2b)(4a+4b)
=8(a-b)^2*(a+b)

Answer 3

(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)(4a 4b)(2a-2b)=8(a-b)²(a b)