Using the Binomial Theorem (10.5.1)

Question 1

• Pascal’s triangle is a group of numbers in a very special pattern, arranged in rows. The top row of Pascal’s triangle is a single 1. The terms in the next row, level 1, are “1 1”. Each subsequent row in Pascal’s triangle contains 1 more term than the preceding row, and each row begins and ends with 1. Each term between the first and last 1 is equal to the sum of the
two terms from the preceding row, that are on either side. So, the level 2 row’s entries are “1 2 1”.

Answer 1

• Pascal’s triangle is a group of numbers in a very special pattern, arranged in rows. The top row of Pascal’s triangle is a single 1. The terms in the next row, level 1, are “1 1”. Each subsequent row in Pascal’s triangle contains 1 more term than the preceding row, and each row begins and ends with 1. Each term between the first and last 1 is equal to the sum of the two terms from the preceding row, that are on either side. So, the level 2 row’s entries are “1 2 1”.

Question 2

• The binomial theorem can be used to find the expansion of a power of a binomial, such as (x + y)
n. It is very useful when the power is greater than 3.

Answer 2

• The binomial theorem can be used to find the expansion of a power of a binomial, such as (x + y)
n . It is very useful when the power is greater than 3.

Question 3

• The binomial theorem states that the coefficients in a binomial expansion follow directly from Pascal’s triangle.

Answer 3

• The binomial theorem states that the coefficients in a binomial expansion follow directly from Pascal’s triangle.