1. 7.1 Pascal’s Triangle and Binomial Theorem 3/18/2013

2. Review

3. Pascal’s Triangle What do you noticed about the coefficients of each term?

4. Pascal’s Triangle Is used to find the coefficients in the expansion of the binomial (a + b) raised to the n th power.

5. Steps in finding (a+b) n : 1.Make n+1 columns. 2.From the Pascal’s Triangle, n th row, write the coefficient in each column. 3.Multiply each coefficient by a starting from a n, decreasing n by 1 in the next column until you reach a in the 2 nd to the last column. 4.Starting in column 2, multiply each column by b increasing its exponent by 1 in the next column until you reach b n in the last column. 5.Simplify.

6. Example: Use Pascal’s Triangle to write the binomial expansion of (x+2) 6. 1 1. Make n + 1 columns (7 columns) 1 2 3 4 5 6 7 2. From the Pascal’s Triangle, 6 th row, write the coefficient in each column. 1 6 15 20 15 6 1 3. Multiply each coefficient by x starting from x 6, decreasing n by 1 in the next column until you reach x in the 2 nd to the last column. (a + b) n 4. Starting in column 2, multiply each column by 2 increasing its exponent by 1 in the next column until you reach 2 6 in the last column. 5. Simplify.

7. Example: Use Pascal’s Triangle to write the binomial expansion of (2y-3) 4. 1 1. Make n + 1 columns (5 columns) 1 2 3 4 5 2. From the Pascal’s Triangle, 4 th row, write the coefficient in each column. 1 4 6 4 1 3. Multiply each coefficient by 2y starting from (2y) 4, decreasing n by 1 in the next column until you reach 2y in the 2 nd to the last column. (a + b) n 4. Starting in column 2, multiply each column by -3 increasing its exponent by 1 in the next column until you reach -3 4 in the last column. 5. Simplify.

8. Homework Worksheet 6.1 Even problems only. “I know a guy who is addicted to brake fluid. He said he can stop anytime.”