Phân tích thành nhân tử: ab(a − b) − ac(a + c) + bc(2a + c − b

Câu 28: Phân tích thành nhân tử: ab(a − b) − ac(a + c) + bc(2a + c − b).

Trả lời

ab(a − b) − ac(a + c) + bc(2a + c − b)

= ab(a − b)− a2c − ac2 + 2abc + bc2 − b2c

= ab(a − b) + (abc − ac2) − (ac2 − bc2) + (abc − b2c)

= ab(a − b) − ac(a − b) − c2(a − b) +  bc(a − b)

= (a − b)(ab – ac − c2 + bc)

= (a − b)[(ab − ac) + (bc − c2)]

= (a − b)[a(b − c) + c(b − c)]

= (a − b)(b − c)(a + c).