Question

(b+c)^3(b-c)+(c+a)^3(c-a)+(a+b)^3(a-b)
factorise it

Answer 1

Answer:

(a-b)3 + (b-c)3 + (c-a)3 = a3 - b3 - 3ab(a-b) + b3 - c3 - 3bc(b-c) + c3 - a3 - 3ca(c-a)

= - 3a2b + 3ab2 - 3b2c + 3bc2 - 3ac2 + 3 a2c = 3 (- a2b + ab2 - b2c + bc2 - ac2 + a2c)

= 3 [(a2(c-b) + (b2(a-c) + (c2(b-a)]

Or

Let x = (a – b), y = (b – c) and z = (c – a)

Consider, x + y + z = (a – b) + (b – c) + (c – a) = 0

⇒ x3 + y3 + z3 = 3xyz

That is (a – b)3 + (b – c)3 + (c – a)3 = 3(a – b)(b – c)(c – a)

hope it will help u