Vocabulary

1
Vocabulary
A way to find coefficients in binomial expansions
(a b)2 where n is a positive integer.
Pascals triangle
n 0 (0th row)
1 1 1 1 ___ 1 1 ___ ___
1 1 ___ ___ ___ 1
n 1 (1st row)
n 2 (2nd row)
n 3 (3rd row)
n 4 (4th row)
The first and last numbers in each row are ___.
Beginning with the second row, every other number
is formed by ________ the two numbers immediately
above the number.
1
adding
2
Vocabulary
Binomial expansion
3
Use Pascals triangle
Example 1
Use the fourth row of Pascals triangle to find
the numbers in the fifth and sixth rows of
Pascals triangle.
Solution
1 4 6 4 1 1 ___ ___
___ ___ 1 1 ___ ___ ___ ___
___ 1
n 4 (4th row)
n 5 (5th row)
n 6 (6th row)
4
Checkpoint. Complete the following exercises.

• Find the numbers in the eighth row of Pascals
  triangle.

1 6 15 20 15 6
1 1 ___ ___ ___ ___ ___ ___
1 1 ___ ___ ___ ___ ___ ___
___ 1
5
Expand a power of a binomial sum
Example 2
Use the Binomial Theorem and Pascals triangle
to write the binomial expansion of (x 5)4.
Solution
The binomial coefficients from the fourth row of
Pascal's triangle are ____, ____. ____, ____, and
____. So the expansion is as follows.
6
Checkpoint. Use the Binomial Theorem and Pascals
triangle to write the binomial expansion.
7
Checkpoint. Use the Binomial Theorem and Pascals
triangle to write the binomial expansion.
8
Expand a power of a binomial difference
Example 3
Use the Binomial Theorem and Pascals triangle
to write the binomial expansion of (x - 6)3.
Solution
The binomial coefficients from the third row of
Pascal's triangle are ____, ____. ____, and ____.
So the expansion is as follows.
9
Checkpoint. Use the Binomial Theorem and Pascals
triangle to write the binomial expansion.
10
Checkpoint. Use the Binomial Theorem and Pascals
triangle to write the binomial expansion.
11
Expand a power of a binomial sum
Example 4
Use the Binomial Theorem and Pascals triangle
to write the binomial expansion of (5 2x)4.
Solution
The binomial coefficients from the fourth row of
Pascal's triangle are ____, ____. ____, ____, and
____. So the expansion is as follows.
12
Checkpoint. Use the Binomial Theorem and Pascals
triangle to write the binomial expansion.
13
Find a coefficient in an expansion
Example 5
Find the coefficient of x3 in (4x 3)4.
Solution
The binomial coefficients from the fourth row of
Pascal's triangle are ____, ____. ____, ____, and
____. So the expansion is as follows.
The coefficients of the x3term is
(___)(___)3(___) _____.
14
Checkpoint. Complete the following exercise.

• Find the coefficient of x2 in the expansion of (7
  - x)5.