Question

phân tích đa thức thành nhân tử

\(a^3\left(b-c\right)+b^3\left(c-a\right)+c^3\left(a-b\right)\)

Answer 1

a³.(b - c) + b³.(c - a) + c³.(a - b)

= a³.(b - c) - b³.(a - c) + c³.(a - b)

= a³.(b - c) - b³.[(b - c) + (a - b)] + c³.(a - b)

= a³.(b - c) - b³.(b - c) - b³.(a - b) + c³.(a - b)

= (a³ - b³)(b - c) - (b³ - c³)(a - b)

= (a - b)(a² + ab + b²)(b - c) - (b - c)(b² + bc + c²)(a - b)

= (a - b)(b - c)(a² + ab + b² - b² - bc - c²)

= (a - b)(b - c)[(a² - c²) +b(a - c)]

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

= (a - b)(b - c)(a - c)(a + b + c)