Phân tích thành nhân tử:

Question

a. A = ab(a - b) + b(b - c) + ca(c - a)

b. B = a(b² - c²) + b(c² - a²) + c(a² - b²)

c. C = (a + b + c)³ - a³ - b³ - c³

Answer 1

a)ab(a−b)+bc(b−c)+ca(c−a)

=a2b−ab2+bc(b−c)+c2a−a2c

=a2(b−c)+bc(b−c)−a(b2−c2)

=a2(b−c)+bc(b−c)−a(b−c)(b+c)

=(b−c)(a2+bc−ab−ac)

=(b−c)[a(a−c)−b(a−c)]

=(b−c)(a−c)(a−b)

c)(a+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+bc)

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

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