\(a^3-a^2c+a^2b-abc=a^2\left(a-c\right)+ab\left(a-c\right)=a\left(a-c\right)\left(a+b\right)\)

\(=a^2\left(a-c\right)+ab\left(a-c\right)\)

\(=a\left(a-c\right)\left(a+b\right)\)

\(=a^2b+ab^2-b^2c-bc^2-ac^2+a^2c\)

\(=a^2\left(b+c\right)+a\left(b-c\right)\left(b+c\right)-bc\left(b+c\right)\)

\(=\left(b+c\right)\left(a^2+ab-ac-bc\right)\)

\(=\left(b+c\right)\left[a\left(a+b\right)-c\left(a+b\right)\right]\)

\(=\left(b+c\right)\left(a+b\right)\left(a-c\right)\)

Ta có b + c = (a + b) + (c – a) nên

A = ab(a + b) – bc[(a + b) + (c – a)] – ac(c – a)

= ab(a + b) – bc(a + b) – bc(c – a) – ac(c – a)

= b(a + b)(a – c) – c(c – a)(b + a)

= (a + b)(a – c)(b + c)

Đáp án cần chọn là: B

ab(a-b) + bc((b-a)+(a-c)) +ac(c-a) 
=ab(a-b) -bc(a-b) -bc(c-a) +ac(c-a) 
=(a-b)(ab-bc) +(c-a)(ac-bc) 
=(a-b) b (a-c) + (c-a) c (a-b) 
=(a-b)(a-c)(b-c) 

\(ab\left(a-b\right)-ac\left(a+c\right)+bc\left(2a-b+c\right)\)

\(=a^2b-ab^2-a^2c-ac^2+2abc-b^2c+bc^2\)

\(=a^2b-ab^2-a^2c-ac^2+abc+abc-b^2c+bc^2\)

\(=\left(bc^2-ac^2+abc-a^2c\right)-\left(b^2c-abc-ab^2+a^2b\right)\)

\(=c\left(bc-ac+ab-a^2\right)-b\left(bc-ac-ab+a^2\right)\)

\(=\left(c-b\right)\left(bc-ac+ab-a^2\right)\)

\(=\left(c-b\right)\left[c\left(b-a\right)+a\left(b-a\right)\right]\)

\(=\left(c-b\right)\left(c+a\right)\left(b-a\right)\)

\(=a^2b-ab^2+b^2c-bc^2+ac^2-a^2c\)

\(=a^2\left(b-c\right)+bc\left(b-c\right)-a\left(b-c\right)\left(b+c\right)\)

\(=\left(b-c\right)\left(a^2-bc-ab-ac\right)\)

\(=\left(b-c\right)\left[a\left(a-b\right)-c\left(a-b\right)\right]\)

Không phân tích được bạn nhé ^^