Who can help me explain how factorization can change symbols? For example, the following question -ab(a-b)^2+a(b-a)^2-ac(a-b)^2 The answer I wrote in my textbook was (a-b) (AB + a-ac) But the answer I'm getting older now is (a-b)^2(ab+a+ac) Note: be sure to tell me how to convert the symbol - 0-~ For example, how to change the symbols in this question? A (A-2) + B (A-2) + C (2-A) how should I use (A-2) as the common factor?

Who can help me explain how factorization can change symbols? For example, the following question -ab(a-b)^2+a(b-a)^2-ac(a-b)^2 The answer I wrote in my textbook was (a-b) (AB + a-ac) But the answer I'm getting older now is (a-b)^2(ab+a+ac) Note: be sure to tell me how to convert the symbol - 0-~ For example, how to change the symbols in this question? A (A-2) + B (A-2) + C (2-A) how should I use (A-2) as the common factor?

-AB (a-b) ^ 2 + a (B-A) ^ 2-ac (a-b) ^ 2
=(a-b)^2[-ab+a-ac]
=(a-b)^2[a-ab-ac]
Obviously, according to your question, it seems that the answer should not be like yours. Here is the main one
(a-b) ^ 2 = (B-A) ^ 2, which can be used as the common factor
If you only convert symbols, you must pay attention to the double anti sign before you invert a factor, so as not to change its previous sign, such as (B-A) = - (a-b), a = - (- a)
A (A-2) + B (A-2) + C (2-A) how should I use (A-2) as the common factor?
Change C (2-A) into - C (A-2)
a(a-2)+b(a-2)+c(2-a)
=a(a-2)+b(a-2)-c(a-2)
=(a-2)(a+b-c)