Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

Add p(p – q), q(q – r) and r(r – p).
(a) p3+q2+r2pq+qrpr
(b) p2+2q2+r2pqqr+pr
(c) p2+q2+r2pqqrpr
(d) p3+q2+r2pqqrpr

Answer
VerifiedVerified
501.6k+ views
like imagedislike image
Hint: Firstly simplify the expression by multiplying the terms in the parentheses using the rule a (b + c) = ab + ac where a, b and c are real numbers. Now apply the property aa=a2 to solve the expression. Then express the algebraic expression according to their decreasing degree of exponents to get the final answer.

Complete step by step solution:
Adding the terms p(p – q), q(q – r) and r(r – p) can be mathematically expressed as,
p(p – q) + q(q – r) + r(r – p)
We know multiplication of an algebraic expression can be done in the form a (b + c) = ab + ac where a, b and c are real numbers.
Applying the above mentioned method to simplify the given expression we get,
pp – pq + qq – qr + rr – rp
We know the property aa=a2 where a is a real number.
Applying the above mentioned property we get,
p2pq+q2qr+r2rp
By arranging the above expression according to the decreasing degree of the exponents we get,
p2+q2+r2pqqrrp
We get the simplified expression as p2+q2+r2pqqrrp.
Hence option (c) is the correct answer.

Note: The possible error that you may encounter can be the incorrect use of operations. The rearranging of operation signs should be done carefully. Multiplying same algebraic terms should be done in accordance with the property aa=a2 where a is a real number.

Latest Vedantu courses for you
Grade 9 | CBSE | SCHOOL | English
Vedantu 9 CBSE Pro Course - (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
Social scienceSocial science
BiologyBiology
ChemistryChemistry
EnglishEnglish
MathsMaths
₹38,500 (9% Off)
₹35,000 per year
Select and buy