P4 Chapter 4 :: Binomial Expansion
www.dilanmaths.com�
Chapter Overview
1:: Binomial Expansion for negative/fractional powers.
2:: Constant is not 1.
3:: Using Partial Fractions
?
?
?
Pure Maths 1 Recap
Do you remember the simple way to find your Binomial coefficients?
?
?
?
?
?
?
?
?
Hopefully you can see the pattern by this point.
Note: You can work out a ‘choose’ value, in the same way, when the top number is negative or fractional, but your calculator can not do this directly.
Binomial Expansion
?
?
When are infinite expansions valid?
Our expansion might be an infinite number of terms. If so, the result must converge
?
?
?
?
?
When are infinite expansions valid?
Expansions are allowed to infinite. However, the result must converge
?
Quickfire Examples:
?
?
?
?
Combining Expansions
Edexcel C4 June 2013 Q2
Firstly express as a product:
?
?
?
Test Your Understanding
C4 Edexcel Jan 2010
?
?
Accuracy of an approximation
?
Exercise 4A
Pearson Pure Mathematics 4
Pages 35-36
Extension
1
Common Errors
?
?
?
?
?
?
?
Quickfire First Step
What would be the first step in finding the Binomial expansion of each of these?
Binomial expansion valid if:
?
?
?
?
?
?
?
?
?
Test Your Understanding
Edexcel C4 June 2013 (Withdrawn) Q1
?
?
Exercise 4B
Pearson Pure Mathematics 4
Pages 38-39
? a
? b
? c
Using Partial Fractions
Partial fractions allows us to split up a fraction into ones we can then find the binomial expansion of.
a
b
c
?
?
?
Test Your Understanding
? a
? b
Exercise 4C
Pearson Pure Mathematics 4
Pages 41-42