Question

Simplify (a2-b2)3+(b2-c2)3c2-a2)3/(a-b)3+(b-c)3+(c-a)3

Answer 1

x3 + y3 + z3 = 3xyz if x+y+z=0

Here in the numerator a2-b2 + b2-c2 + c2-a2 =0

Therefore the numerator = 3(a2-b2)(b2-c2)(c2-a2)

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

Here in the denominator , a-b+b-c+c-a = 0

therefore the denominator = 3 (a-b)(b-a)(c-a)

Therefore Nr/Dr = (a+b)(b+c)(c+a)