Question

Factorize p^3+pqr-1/27q^3+r^3

Answer 1

Answer:

Let p(q - r) = a, q(r - p) = b and r(p - q) = c,

=> a + b + c = 0

=> a + b = - c

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

=> a^3 + b^3 + 3ab(a + b) + c^3 = 0

=> a^3 + b^3 + c^3 = 3abc (because a + b = - c)

Now, p3(q – r)3 + q3(r – p)3 + r3(p – q)3 =

a^3 + b^3 + c^

= 3abc

= 3pqr(p - q)(q - r)(r - p)