Essential Questions

1
Essential Questions

• How do we use the Binomial Theorem to expand a
  binomial raised to a power?
• How do we find binomial probabilities and test
  hypotheses?

2
You used Pascals triangle to find binomial
expansions in Lesson 6-2. The coefficients of the
expansion of (x y)n are the numbers in Pascals
triangle, which are actually combinations.
3
The pattern in the table can help you expand any
binomial by using the Binomial Theorem.
4
Example 1 Expanding Binomials
Use the Binomial Theorem to expand the binomial.
(a b)5
The sum of the exponents for each term is 5.
(a b)5 5C0a5b0
5C1a4b1
5C2a3b2
5C3a2b3
5C4a1b4
5C5a0b5
5
Example 2 Expanding Binomials
Use the Binomial Theorem to expand the binomial.
(2x y)3
(2x y)3 3C0(2x)3y0
3C1(2x)2y1
3C2(2x)1y2
3C3(2x)0y3
6
(No Transcript)
7
Example 3 Expanding Binomials
Use the Binomial Theorem to expand the binomial.
(x y)5
(x y)5 5C0x5(y)0
5C1x4(y)1
5C2x3(y)2
5C4x1(y)4
5C3x2(y)3
5C5x0(y)5
8
Example 4 Expanding Binomials
Use the Binomial Theorem to expand the binomial.
(a 2b)3
3C1a2(2b)1
(a 2b)3 3C0a3(2b)0
3C3a0(2b)3
3C2a1(2b)2
9
Lesson 3.3 Practice A