The identity a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−bc−ca)
can be easily verified by expanding the right hand side.
Using the above identity (or otherwise) answer the following:
Factorize the expression:
(p+2q−3r)3+(q+2r−3p)3+(r+2p−3q)3
(a) (p+q+r)(p2+q2+r2−2(pq+qr+pq))
(b) (p+q+r)(2p2+2q2+2r2−3(pq+qr+rp))
(c) 3(p+2q−3r)(q+2r−3p)(r+2p−3q)
(d) None of these
The identity a3+b3+c3−3abc=(a+b+c)(a2+b2+c2−ab−bc−ca)
can be easily verified by expanding the right hand side.
Using the above identity (or otherwise) answer the following:
Factorize the expression:
(p+2q−3r)3+(q+2r−3p)3+(r+2p−3q)3
(a) (p+q+r)(p2+q2+r2−2(pq+qr+pq))
(b) (p+q+r)(2p2+2q2+2r2−3(pq+qr+rp))
(c) 3(p+2q−3r)(q+2r−3p)(r+2p−3q)
(d) None of these
Harshit Singh , 3 Years ago
Grade 12th pass
