Are these Binomial Theorem notes free?

Yes. The full 3-page Binomial Theorem sheet is free inside CapCompass, which runs in your browser with no account needed.

What does the Binomial Theorem revision sheet cover?

What the theorem gives, The binomial theorem, full expansion, the general term, (k+1)th in the sum, Pascal's triangle, each entry is the sum of the two entries above it, the two outer entries of every row, The first four rows of Pascal's triangle, n=0, n=1, n=2, n=3.

Is this for Class 11 CBSE Mathematics?

It is written from the NCERT syllabus, so it serves CBSE and any board that follows NCERT for Mathematics.

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Binomial Theorem — Class 11 CBSE Mathematics revision notes

A 3-page visual revision sheet for Binomial Theorem, written for Class 11 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.

Binomial Theorem revision notes, page 1 of 3 — A preview of page 1 — all 3 pages open full size in the app.

Binomial Theorem in one look

expanding (a+b)^n without multiplying it out by hand

What the theorem gives

(a+b)^n expands into n+1 terms: a coefficient, a power of a, a power of b
a's power falls n to 0, b's rises 0 to n: they add to n
the coefficients are the combinations nC0 to nCn, the numbers counted last chapter

The binomial theorem

full expansion (a+b)^n=Σ_k=0^n ^nC_k a^n-kb^k
the general term, (k+1)th in the sum T_k+1= ^nC_k a^n-kb^k

Pascal's triangle

each entry is the sum of the two entries above it ^nC_r= ^n-1C_r-1+ ^n-1C_r
the two outer entries of every row ^nC_0= ^nC_n=1

The first four rows of Pascal's triangle

n=0: 1
n=1: 1 1
n=2: 1 2 1
n=3: 1 3 3 1

Page 1 of 3. The full sheet, all 3 pages, opens free in the app.

What this Binomial Theorem sheet covers

What the theorem gives
The binomial theorem
full expansion
the general term, (k+1)th in the sum
Pascal's triangle
each entry is the sum of the two entries above it
the two outer entries of every row
The first four rows of Pascal's triangle
n=0
n=1
n=2
n=3
The coefficients are symmetric
Middle term: one, or two
n even, row 4
n odd, row 5
Term independent of x
A specific term with a coefficient inside
Two quick special sums
Symbols
Traps that cost marks
Tricks that save time

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