The document provides an explanation of the binomial theorem formula for finding a specific term in the expansion of a binomial expression. It gives the formula as: ⎛ n ⎞ n−r r ⎜ r ⎟ x y ⎝ ⎠ Where n is the total number of terms, r is 1 less than the term number being found, x and y are the terms being added or subtracted. It provides an example of finding the 5th term of (a + b)6. It also provides an example of finding the 5th term of (3x - 5y)

1. 11.6 The Binomial Theorem
Day Two
Hebrews 4:16 "Let us therefore come boldly unto the throne
of grace that we may obtain mercy, and find grace to help in
time of need."

2. From the Binomial Theorem, a specific
term is represented by:
⎛ n ⎞ n−r r
⎜ r ⎟ x y
⎝ ⎠

3. From the Binomial Theorem, a specific
term is represented by:
⎛ n ⎞ n−r r
⎜ r ⎟ x y
⎝ ⎠
(note: r is 1 less than the term number)

4. From the Binomial Theorem, a specific
term is represented by:
⎛ n ⎞ n−r r
⎜ r ⎟ x y
⎝ ⎠
(note: r is 1 less than the term number)
This formula is a variation of what is in your book.

5. Example: Find the 5th term of ( a + b )
6

6. Example: Find the 5th term of ( a + b )
6
n=6 r=4

7. Example: Find the 5th term of ( a + b )
6
n=6 r=4
⎛ 6 ⎞ 2 4
⎜ 4 ⎟ ab
⎝ ⎠
2 4
15a b

8. Example: Find the 5th term of ( a + b )
6
n=6 r=4
⎛ 6 ⎞ 2 4
⎜ 4 ⎟ ab
⎝ ⎠
2 4
15a b
6 5 1 4 2 3 3 2 4 1 5 6
a + 6a b + 15a b + 20a b + 15a b + 6a b + b
term 5

9. Groups: Find the 5th term of ( 3x − 5y )
10

10. Groups: Find the 5th term of ( 3x − 5y )
10
n = 10 r=4
⎛ 10 ⎞ 6 4
⎜ 4 ⎟ ab
⎝ ⎠
⎛ 10 ⎞ 6 4
⎜ 4 ⎟ ( 3x ) ( −5y )
⎝ ⎠
⎛ 10 ⎞ 6 4 6 4
⎜ 4 ⎟ ( 3) ( −5 ) x y
⎝ ⎠
6 4
95,681,250x y

11. Groups: Find the term that contains x in
4
the expansion of ( 3x + y )
15

12. Groups: Find the term that contains x in
4
the expansion of ( 3x + y )
15
n = 15 r = 11
⎛ 15 ⎞ 4 11
⎜ 11 ⎟ ( 3x ) y
⎝ ⎠
4 11
110,565x y

13. HW #12
“If we take people as we find them, we may make them
worse, but if we treat them as though they are what
they should be, we help them to become what they are
capable of becoming.” Johann Wolfgang von Goethe