May 22, 2015
(9.2) The Binomial Theorem
Objective: To expand binomials using the Binomial Theorem and
Pascal's Triangle.
Why: The Binomial Theorem is a useful study in combinatorial
patterns.
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
Expand.
(x + y)o
(x + y)1
(x + y)2
(x + y)3
(x + y)4
May 22, 2015
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
Pascal's Triangle
1
row 0
row 1
1
row 2
1
row 3
1
row 4
1
row 5
1
row 6
3
10
15
1
1
3
6
4
5
6
1
2
1
10
20
1
4
5
1
15
6
1
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
The Binomial Theorem gives a way to find the coefficient
of each term of expansion using combinations.
(x+y)n = nC0xny0 + nC1xn-1y1 + nC2xn-2y2 + ... + nCnx0yn
where nCr =
n!
(n-r)!r!
n
r
=
(n elements taken r at a time)
Ex. (x + y)3 = (x + y)(x + y)(x + y)
3
2
1
1
2
0
= 3C0 x y 0 + 3C1 x y + 3C 2 x y + C
x y
3 3
3
May 22, 2015
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
Evaluate.
1.
8
C2
3. C 0
7
2. 10
3
4.
C
7
3
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
Use the Binomial Theorem to expand.
5. (x+1) 5
May 22, 2015
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
6. (2y - 4)
4
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
7. Find the coefficient, a, in
(4x - y) 10
ax2y 8 for
May 22, 2015
Expand the binomial.
Name: ___________________
(3x - 2y)4
Do Now Please:
*Take problem out of the front basket and complete.
May 22, 2015
Expand the binomial.
Name: ___________________
(3x - 2y)4
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
8. Find the 6th term of (a+2b) 8
May 22, 2015
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
HW:
(REG) (9.2) Pg.648: 3, 6, 13, 15, 20, 24
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.
May 22, 2015
Obj: To expand binomials using the Binomial Theorem and Pascal's Triangle.