08 binomial expansion

Question 1

What is Pascal’s triangle used for?

Answer 1

Finding the coefficients of expanded binomial term.

Question 2

What is the pattern of (a+b)* expanded?

Answer 2

The power of a decreases along the term, the power of b increases across the term.

Question 3

What does Pascal’s triangle look like?

Answer 3

. 1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

Question 4

What does ‘!’ Mean ?

Answer 4

factorial, for example 5! Is 5x4x3x2x1.

Question 5

How would you express all the different ways that ‘abcde’ can be ordered?

Answer 5

5!.

Question 6

How would you express all the different ways ‘abcaa’ can be ordered?

Answer 6

5!/3!, this is because there is 3 of the same letter.

Question 7

How would you express all the different ways ‘abbaa’ can be ordered?

Answer 7

5!/3!x2!, this is because there are 3 a’s and 2 b’s. Therefore you multiply them together and divide by this.

Question 8

How does factorials link back to binomial expansion?

Answer 8

abbaa -> a3b2

The combinations of abbaa and be wrote as 5!/3!x2!, this is the coefficient of the term a3b2.

Question 9

What is the formula used for binomial expansion?

Answer 9

n (n).
C = ( ) = n!/r!(n-r)!
r (r)