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# 1115 ch 11 day 15

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### 1115 ch 11 day 15

1. 1. 11.6 The Binomial Theorem Day TwoHebrews 4:16 "Let us therefore come boldly unto the throneof grace that we may obtain mercy, and ﬁnd grace to help intime of need."
2. 2. From the Binomial Theorem, a speciﬁcterm is represented by: ⎛ n ⎞ n−r r ⎜ r ⎟ x y ⎝ ⎠
3. 3. From the Binomial Theorem, a speciﬁcterm is represented by: ⎛ n ⎞ n−r r ⎜ r ⎟ x y ⎝ ⎠ (note: r is 1 less than the term number)
4. 4. From the Binomial Theorem, a speciﬁcterm 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. 5. Example: Find the 5th term of ( a + b ) 6
6. 6. Example: Find the 5th term of ( a + b ) 6 n=6 r=4
7. 7. Example: Find the 5th term of ( a + b ) 6 n=6 r=4 ⎛ 6 ⎞ 2 4 ⎜ 4 ⎟ ab ⎝ ⎠ 2 4 15a b
8. 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. 9. Groups: Find the 5th term of ( 3x − 5y ) 10
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. 11. Groups: Find the term that contains x in 4 the expansion of ( 3x + y ) 15
12. 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. 13. HW #12“If we take people as we ﬁnd them, we may make themworse, but if we treat them as though they are whatthey should be, we help them to become what they arecapable of becoming.” Johann Wolfgang von Goethe