Question

factorise ab(a-b)+bc(b-c)+ca(c-a)​

Answer 1

Factor: .ab(a−b)+bc(b−c)+ca(c−a)

Expand: a2b−ab2+b2c−bc2+ac2−a2c

Arrange the terms like this: a2b−a2cterms with a2+ac2−ab2terms with a+b2c−bc2terms with no a

Factor: a2(b−c)−a(b2−c2)+bc(b−c)

. . . =a2(b−x)−a(b−c)(b+c)+bc(b−c)

. . . =(b−c)[a2−a(b+c)+bc]

. . . =(b−c)[a2−ab−ac+bc]

. . . =(b−c)[a(a−b)−c(a−b)]

. . . =(b−c)(a−b)(a−c)

Answer 2

ANSWER

-(a-b)(b-c)(c-a)