Question

Factorise:(p-q)^3+(q-r)^3+(r-p)^3​

Answer 1

Question :-

Factorize (p-q)³ + (q-r)³ + (r-p)³

Identity to use :-

a³+b³+c³ = 3abc if a+b+c = 0

Let us check if the terms add up to 0,

(p-q)+(q-r)+(r-q)

Removing the brackets

=> p-q+q-r+r-p

Grouping all the like terns,

=> p-p+q-q+r-r

=> 0.

Hence here the identity can be used.

Answer :- 3[(p-q)(q-r)(r-p)]

Hope it helps

Happy day!