1. The Binomial Theorem

2. The Binomial Theorem

3. The Binomial Theorem The powers on “a” start with n and decrease.
has n+1 terms.
The powers on “a” start with n and decrease.
The powers on “b” start with 0 and increase.
The sum of the powers in each term add to n.
The coefficients start and end with 1.
The coefficients follow Pascal’s Triangle.
The coefficients can be found with combinations.

4. The Binomial Theorem

5. The Binomial Theorem

6. A couple marries and has three children. (Note the order
A couple marries and has three children. (Note the order!) What are the probabilities of each possible combination of boys and girls?

7. Calculate the Binomial Expansion…
3 boys & 0 girls =
2 boys & 1 girl =
1 boy & 2 girls =
0 boys & 3 girls =
1/8
3/8
3/8
1/8

8. The Binomial Theorem

9. Finding the Coefficient of a Specific Term
Find the coefficient of the x4y8 term in the expansion of (x + y)12.
Find the coefficient of the a5 term
in the expansion of (a – 4)14.