(628)-272-0788 info@etutorworld.com
Select Page

Binomial Theorem

Home » Online Math Tutoring » Algebra1-Tutoring » Binomial Theorem

Binomial theorem is a theorem developed for calculating any power of any binomial without actually multiplying at length.

General binomial expansion is denoted by


(a+b)=nc0an +nc1an-1b+nc2an-2b2+…………………..+ncn-1abn-1+ncnbn  where n>=0 and

Example (x+y)3=3c0x3+3c1x2y+3c2xy2+3c2y3

Example – Expand (p+1)3


=  p3+3p2+3p+1

Some Facts about Binomial Theorem

  • General term for an expansion (a+b)n is Tr+1 =ncran-rbis , where 0 <= r<= n.
  • Number of terms in expansion will be n + 1.

Check Point:

Expand the following binomials –

1) (a+b)3

2) (s+3)3

3) (y2+1)4

4) (3+x)4

5) (z+2)6

Answer Key

1) a3+3a2b+3b2a+b3

2)  s3+9s2+27s+27

3) y8+4y6+6y4+4y2+1

4) 81+108x+54x2+12x3+x4

5) z6+12z5+60z4+160z3+240z2+192z+64

Personalized Online Tutoring

eTutorWorld offers affordable one-on-one live tutoring over the web for Grades 2-12, Test Prep help for Standardized tests like SCAT, CogAT, SSAT, SAT, ACT, ISEE and AP. You may schedule online tutoring lessons at your personal scheduled times, all with a Money-Back Guarantee. The first one-on-one online tutoring lesson is always FREE, no purchase obligation, no credit card required.

For answers/solutions to any question or to learn concepts, take a FREE Demo Session.

No credit card required, no obligation to purchase.
Just schedule a FREE Sessions to meet a tutor and get help on any topic you want!

Learn more about Scientific Method and other important topics with 7th Grade Science Tutoring at eTutorWorld. Our expert science tutors break down the topics through interactive one-to-one sessions. We also offer the advantage of customized lesson plans, flexible schedules and convenience of learning from home.

Pricing for Online Tutoring

Tutoring Package Validity Grade (1-12), College
5 sessions 1 Month $124
1 session 1 Month $25
10 sessions 3 months $239
15 sessions 3 months $354
20 sessions 4 months $449
50 sessions 6 months $1049
100 sessions 12 months $2049
Which Pack is the best one for your Child ?
Take the quiz and get a personalized recommendation