Question

Phân tích đa thức thành nhân tử:

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

Answer 1

(a+b+c)3−a3−b3−c3(a+b+c)3−a3−b3−c3

=a3+3a2(b+c)+3a(b+c)2+(b+c)3−a3−b3−c3=a3+3a2(b+c)+3a(b+c)2+(b+c)3−a3−b3−c3

=3(b+c)(a2+ab+ac)+b3+3b2c+3bc2+c3−b3−c3=3(b+c)(a2+ab+ac)+b3+3b2c+3bc2+c3−b3−c3

=3(b+c)(a2+ab+ac+bc)=3(b+c)(a2+ab+ac+bc)

=3(b+c)[a(a+b)+c(a+b)]=3(b+c)[a(a+b)+c(a+b)]

=3(b+c)(a+b)(a+c)