Sign In | Starter Of The Day | Tablesmaster | Fun Maths | Maths Map | Topics | More

International Baccalaureate Mathematics

Number and Algebra

Syllabus Content

The binomial theorem including the expansion of (a+b)n,n ∈ N. Use of Pascal's triangle and nCr

Here are some specific activities, investigations or visual aids we have picked out. Click anywhere in the grey area to access the resource.

Here are some exam-style questions on this statement:

See all these questions

Click on a topic below for suggested lesson Starters, resources and activities from Transum.


Furthermore

Official Guidance, clarification and syllabus links:

Counting principles may be used in the development of the theorem.

\(^nC_r\) should be found using both the formula and technology.

Example: Find \(r\) when \(^6C_r=20\), using a table of values generated with technology.

Formula Booklet:

Binomial theorem \(n \in \mathbb{N} \)

$$ (a + b)^n = a^n +\;^nC_1 a^{n-1}b + \ldots + \;^nC_r a^{n-r}b^r + \ldots + b^n $$ $$ ^nC_r = \frac{n!}{r!(n-r)!} $$

Example

To expand \( (2x + 3y)^5 \) using the binomial theorem, we can use the formula:

$$ (a + b)^n = a^n + nC_1 a^{n-1}b + \ldots + nC_r a^{n-r}b^r + \ldots + b^n $$

Substituting \( a = 2x \), \( b = 3y \), and \( n = 5 \) into the formula, we get:

$$ (2x + 3y)^5 = (2x)^5 + 5C_1 (2x)^4(3y) + 5C_2 (2x)^3(3y)^2 + 5C_3 (2x)^2(3y)^3 + 5C_4 (2x)(3y)^4 + (3y)^5 $$

Simplifying further:

$$ (2x + 3y)^5 = 32x^5 + 160x^4 \cdot 3y + 80x^3 \cdot 9y^2 + 40x^2 \cdot 27y^3 + 10x \cdot 81y^4 + 243y^5 $$

Which results in:

$$ (2x + 3y)^5 = 32x^5 + 480x^4y + 720x^3y^2 + 1080x^2y^3 + 810xy^4 + 243y^5 $$

This video on the Binomial Theorem is from Revision Village and is aimed at students taking the IB Maths AA Standard level course

How do you teach this topic? Do you have any tips or suggestions for other teachers? It is always useful to receive feedback and helps make these free resources even more useful for Maths teachers anywhere in the world. Click here to enter your comments.


Apple

©1997-2024 WWW.TRANSUM.ORG