The Binomial Expansion (C5)

Question 1

What is Pascals Triangle and what does it show?

Answer 1

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

It shows the coefficients for a binomial expansion, with the row being the power (n).

Question 2

What will be the difference in expansion between ( 1 + x )^3 and ( 1 - x )^3 ?

Answer 2

( 1 - x )^3 will have the same terms, although the terms without any power of x or with an odd power of x will be negative, including 1 because ( - 1 )^0 is +1.

Question 3

What is the formula for Binomial Expansion ?

Answer 3

(a + b)^n = (nCk) X a^(n-k) X b^k

This is where k is a term increasing by 1 from 0 for every consecutive term in the expansion.

Question 4

What is a formula you can use to find a Binomial Expansion which uses Pascal’s Triangle?

Answer 4

( a + b)^n = y X a^n X b^k
This is where k is a term increasing by 1 from 0 for every consecutive term in the expansion. n is also reduced by 1 for every consecutive term in the expansion.