This document discusses binomial expansion using Pascal's triangle and the binomial theorem. It explains that a binomial is a polynomial with two terms and the binomial theorem allows for quick expansion of binomial expressions raised to a power. It provides examples of using the binomial theorem to expand binomial expressions up to the x^3 term for different types of binomial questions, including a standard binomial, fractional binomial, and binomial with a square root.

1. Binomial expansion
Summary:
What is a binomial?
 A binomial is a polynomial with two terms (polynomial just means many terms).
This is a binomial
Pascal's Triangle
 Pascal's Triangle is 1 way of expanding a binomial.
 To build the triangle, start with "1" at the top, then continue placing numbers
below it in a triangular pattern.
 The two numbers adding with each other should be equal to the number below
Binomial theorem
 The Binomial Theorem is a quick way of expanding a binomial expression that has
been raised to some power. This power is usually something inconveniently large.
 Most people prefer to use this method of expanding than Pascal's Triangle since
it’s much quicker. In addition, pascal’s triangle is used for small powers.

2. Type of Binomial Questions
 for part A, you should use the binomial theorem on (1+2x) ^3 (Equation stated
above). You can use Pascale’s triangle to work out this equation but it would be
time consuming.
 Replace n with 3 and x with 2x
 Since the question has asked us to expand up to x^3, any values beyond this
will not be included in our answer
 2) for part B, Our binomial is a fraction. For these type of questions, you should
inverse our binomial. This will give us (1-x) ^-1
 After you have inversed the binomial, you can now use the binomial theorem to
find our terms up to x^3
 Replace n with -1 and x with –x
 Any values beyond x^3 will not be included in our answer

3.  3) For part C, our binomial has a square root. From our knowledge of roots, we can
write this as (1+x) ^1/2
 Now that our binomial is in index form, we can use binomial theorem to work out
terms up to x^3
 Replace n with ½ and x with x