Binomial expansion

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Last updated 3:37 PM on 9/22/26
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4 Terms

1
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What is it?

A quick way to multiply multiple two term brackets. (a+b)^n

2
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How does pascals triangle work and how is it used within binomial expansion

  • It is the sum of the two terms above

  • The two terms on the outside must be 1

  • it can also be written out with permutations through the rows as e.g the third row of 1,3,3,1 can also be shown as 3C0 - 1 3C1 - 3 3C2 - 3 3C3 - 1

  • This means the permutations can be replaced by Pascals triangle when doing binomial expansion


<ul><li><p>It is the sum of the two terms above </p></li><li><p>The two terms on the outside must be 1</p></li><li><p>it can also be written out with permutations through the rows as e.g the third row of 1,3,3,1 can also be shown as 3C0 - 1 3C1 - 3 3C2 - 3 3C3 - 1</p></li><li><p>This means the permutations can be replaced by Pascals triangle when doing binomial expansion</p></li></ul><p></p>
3
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How to do it?

e.g: (1-2x)³

= 1(1³)(-2x)^0

+ 3(1²)(-2x)^1

+ 3(1³)(-2x)²

+ 1(1^4)(-2x)³


(the 1,3,3,1 order is the same as pascals triangle 4th row which is why you multiply it by that in order from left to right)


4
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What is an example of a factorial

e.g. 4!

4×3×2×1