Phân tích đa thức thành nhân tử: a, -c^2(a-b)+b^2(a-c)-a^2(b-c) b, 4a^2b^2(2a+b)+b^2c^2(c-b)-4C^2a^2(2a+c) c, bc(a+d)(b-c)-ac(b+d)(a-c)+ab(c+d)(a-b)

Giải thích các bước giải:

`a)`

`-c^2(a - b) + b^2(a - c) - a^2(b - c)`

`= -ac^2 + bc^2 + ab^2 - b^2c - a^2b + a^2c`

`= a^2c - ac^2 + bc^2 - a^2b + ab^2 - b^2c`

`= ac(a - c) + b(c^2 - a^2) + b^2(a - c)`

`= ac(a - c) + b(c - a)(c + a) + b^2(a - c)`

`= ac(a - c) - b(a - c)(c + a) + b^2(a - c)`

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

`= (a - c)[c(a - b) - b(a - b)]`

`= (a - c)(a - b)(c - b)`

`b)`

`4a^2b^2(2a + b) + b^2c^2(c - b) - 4c^2a^2(2a + c)`

`= 8a^3b^2 + 4a^2b^3 + b^2c^3 - b^3c^2 - 8c^2a^3 - 4c^3a^2`

`= 8a^3b^2 - 8c^2a^3 - b^3c^2 + b^2c^3 + 4a^2b^3 - 4c^3a^2`

`= 8a^3(b^2 - c^2) - b^2c^2(b - c) + 4a^2(b^3 - c^3)`

`= 8a^3(b - c)(b + c) - b^2c^2(b - c) + 4a^2(b - c)(b^2 + bc + c^2)`

`= (b - c)[8a^3(b + c) - b^2c^2 + 4a^2(b^2 + bc + c^2)]`

`c)`

`bc(a + b)(b - c) - ac(b + d)(a - c) + ab(c + d)(a - b)`

`= bc(ab - ac + b^2 - bc) - ac(ab - bc + ad - cd) + ab(ac - bc + ad - bd)`

`= ab^2c - abc^2 + b^3c - b^2c^2 - a^2bc + abc^2 - a^2cd + ac^2d + a^2bc - ab^2c + a^2bd - ab^2d`

`= ab^2c - ab^2c - abc^2 + abc^2 - a^2bc + a^2bc + b^3c - b^2c^2 - a^2cd + ac^2d + a^2bd - ab^2d`

`= b^3c - b^2c^2 - a^2cd + ac^2d + a^2bd - ab^2d`

`= b^2c(b - c) - ad(ac - c^2 - ab + b^2)`

`= b^2(b - c) - ad(-ab + ac + b^2 - c^2)`

`= b^2(b - c) - ad[-a(b - c) + (b - c)(b + c)]`

`= b^2(b - c) - ad(b - c)(-a + b + c)`

`= (b - c)[b^2 - ad(-a + b + c)]`