Chapter 8 The Binomial Expansion - Year 1 Flashcards
What is Pascals triangle?
A triangle of numbers that can be used to find the expansions binomial brackets
How do you calculate Pascals Triangle?
The edges are always 1 and you get the next term by adding the 2 above it
What is a general rule or Pascals Triangle?
It is 1 extra than you would think
How do you use Pascals triangle to expand binomials?
You go to the row of Pascals triangle that is 1 more than the power on the bracket
Now you right them down the side of your page
Then you write down the first number in the bracket next to the numbers
You put each of those numbers to the power of the bracket and decrease the power by 1 until you get to 0
Then you put the second term in bracket next in the list
Then, starting at 0, you increase the power on that term by 1 at a time
Then you write out the full answer beneath it
How do you use pascals triangle to expand a binomial multiplied by another binomial
You calculate the first bracket (with the higher power) then use simple bracket expansion techniques to expand to get the final answer
If you are given a binomial with an unknown in it and you are told what the x^2 term will be how do you work it out?
Whatever the power of the bracket is you go to the time +1 of that
Since it is to the power of 2 you go 3 in
Since the powers in each term must add to the power of the bracket you know what the power of the first term of the binomial will be
You then multiply those 2 number together as well with the constant in pascals triangle and say that it is equal to whatever the question saysx^2
And solve
If one term is 6X bigger than another what do you know?
If you times the other term by 6 then they will be equal
What special button do you need to know?
How do you use it?
What does it look like?
The “choose” button
You press shift then the divide button
It looks like c
What is factor notation?
How do you work out the x^n term in the expansion of an binomial?
You write down the x term with its power that you want
Then write down the first term in the binomial to the power of (the power of the binomial - the power on the x term)
Then write down (the number of the power on the binomial) choose (the power on the x term)
Then calculate it
What does this equal?
What does this equal?
What chooses are equal?
What do you know about the powers in each term of a binomial expansion?
The powers in each term will sum to the power of the bracket
How do you use use factor notation to calculate binomial expansion?
You start off with n (the power on the bracket) choose 0
Now you right them down the side of your page increasing 0 by 1 each time until 0 becomes n
Then you write down the first number in the bracket next to the numbers
You put each of those numbers to the power of the bracket and decrease the power by 1 until you get to 0
Then you put the second term in bracket next in the list
Then, starting at 0, you increase the power on that term by 1 at a time
Then you write out the full answer beneath it
What is key to remember if you need to do binomial expansion with unknown powers?
