Question

25.
Factorize : (p-q)^3 + (q-n)^3 + (r-p)^3​

Answer 1

Answer:

Step-by-step explanation:

Note that p=q makes the value of the expression 0. Therefore p-q is a factor. Symmetry guarantees that q-r and r-p are also factors. The degree of the expression is 3 and the degree of (p-q)(q-r)(r-p) is also 3. Therefore

(p−q)3+(q−r)3+(r−p)3=K(p−q)(q−r)(r−p)

where K is some number.

It is not complicated to continue. The expression, when expanded contains a  3p2q . The coefficient of  p2q , in the proposed factored form is K and so K=3. Thus

(p−q)3+(q−r)3+(r−p)3=3(p−q)(q−r)(r−p)

233 viewsView 2 Upvoters · Answer requested by Quora User