Phân tích đa thức thành nhân tử: A = ab(a + b) – bc(b + c) + ac (a – c).

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

= a²b + ab² – b²c – bc² + a²c – ac²

= (a²b + a²c) + (ab² – ac²) – (b²c + bc²)

= a²(b + c) + a(b² – c²) – bc(b + c)

= a²(b + c) + a(b + c)(b – c) – bc(b + c)

= (b + c)[a² + a(b – c) − bc]

= (b + c)(a² + ab – ac − bc)

= (b + c)[a(a + b) – c (a + b)]

= (b + c)(a + b)(a – c).