IB Mathematics Analysis and Approaches Topic SL 1.9—binomial Theorem Where n Is an Integer Revision Notes (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 1.9—binomial Theorem Where n Is an Integer Revision Notes (SL/HL) | RevisionDojo

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The Binomial Theorem

The binomial theorem is a method for expanding powers of binomials.
For any positive integer $n$, it gives the expansion of $(a+b)^n$ as a sum of terms involving powers of $a$ and $b$.

Pascal's Triangle and nCr Notation

Pascal's Triangle

Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra.
Each number is the sum of the two numbers directly above it.

Note

The numbers in Pascal's triangle correspond to the coefficients in the binomial expansion.
The nth row (starting with row 0 at the top) gives the coefficients of the expansion of $(a+b)^n$.

Tip

It's worth memorizing the first few rows of Pascal's triangle, up to the 6th row (1, 5, 10, 10, 5, 1).
This will help you expand any binomial power up to $(a + b)^5$.

Note

We'll talk about Pascal's triangle later in the section on calculating binomial coefficients.

nCr Notation

The notation $^nC_r$ (or $\binom{n}{r}$) represents the number of ways to choose $r$ items from a set of $n$ items, where order doesn't matter.
It's read as "n choose r".

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The Binomial Theorem

The binomial theorem is a method for expanding powers of binomials.
For any positive integer $n$, it gives the expansion of $(a+b)^n$ as a sum of terms involving powers of $a$ and $b$.

Pascal's Triangle and nCr Notation

Pascal's Triangle

Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra.
Each number is the sum of the two numbers directly above it.

Note

The numbers in Pascal's triangle correspond to the coefficients in the binomial expansion.
The nth row (starting with row 0 at the top) gives the coefficients of the expansion of $(a+b)^n$.

Tip

It's worth memorizing the first few rows of Pascal's triangle, up to the 6th row (1, 5, 10, 10, 5, 1).
This will help you expand any binomial power up to $(a + b)^5$.

Note

We'll talk about Pascal's triangle later in the section on calculating binomial coefficients.

nCr Notation

The notation $^nC_r$ (or $\binom{n}{r}$) represents the number of ways to choose $r$ items from a set of $n$ items, where order doesn't matter.
It's read as "n choose r".

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Number and Algebra16 subtopics

Functions16 subtopics

Geometry & Trigonometry18 subtopics

Statistics & Probability14 subtopics

Calculus19 subtopics

IB Mathematics Analysis and Approaches SL 1.9—binomial Theorem Where n Is an Integer Notes

The Binomial Theorem

Pascal's Triangle and nCr Notation

Pascal's Triangle

nCr Notation

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The Binomial Theorem

Pascal's Triangle and nCr Notation

Pascal's Triangle

nCr Notation

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Excepteur sint occaecat cupidatat non proident

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Number and Algebra16 subtopics

Functions16 subtopics

Geometry & Trigonometry18 subtopics

Statistics & Probability14 subtopics

Calculus19 subtopics