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Question
Factorise: (p − q)3 + (q − r)3 + (r− p)3
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Solution
(p − q)3 + (q − r)3 + (r− p)3
Let p − q = x
q − r = y
r− p = z
Therefore, x + y+ z = p − q + q − r + r − p = 0
So,
(p − q)3 + (q − r)3 + (r− p)3 = x3 + y3 + z3
= 3xyz (when x + y + z = 0, then x3 + y3 + z3 = 3xyz )
= 3(p − q)(q − r)(r− p)
Let p − q = x
q − r = y
r− p = z
Therefore, x + y+ z = p − q + q − r + r − p = 0
So,
(p − q)3 + (q − r)3 + (r− p)3 = x3 + y3 + z3
= 3xyz (when x + y + z = 0, then x3 + y3 + z3 = 3xyz )
= 3(p − q)(q − r)(r− p)
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