Chapter 9

Question 1

Define binomial expression.

Answer 1

Two terms.

Question 2

What patterns are there for the expansion of (a+b)^n where n= 0-4?

Answer 2

.The powers of each term sum to n.
.Each power of a and b present - complementary.
.Symmetrical pattern of coefficients.

Question 3

What is the binomial theorem?

Answer 3

(a+b)^n = nC0a^nb^0 + nC1a^n-1b^1 + … + nCna^0b^n.

Question 4

What is a binomial coefficient?

Answer 4

nCr - constants in the expansion.

Question 5

What can you use for finding these coefficients?

Answer 5

Pascal’s Triangle.

Question 6

What is n!?

Answer 6

n! = n x (n-1) x … x 2 x 1 where n EN.

Question 7

What is 0! ?

Answer 7

1.

Question 8

What is the nCr formula?

Answer 8

nCr = n!/r!(n-r)!

Question 9

What is the value of nC0?

Answer 9

1.

Question 10

What is the value of nC1?

Answer 10

n.

Question 11

What is the value of nC2?

Answer 11

n(n-1)/2.

Question 12

What happens to large powers of x when x is close to zero?

Answer 12

They will be really small.

Question 13

What is a use of binomial expansion?

Answer 13

Estimating values of decimals to powers e.g. 3.27^5.