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

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Presentation transcript:

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

Review

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

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

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.

Example: Use Pascal’s Triangle to write the binomial expansion of (x+2) Make n + 1 columns (7 columns) From the Pascal’s Triangle, 6 th row, write the coefficient in each column 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.

Example: Use Pascal’s Triangle to write the binomial expansion of (2y-3) Make n + 1 columns (5 columns) From the Pascal’s Triangle, 4 th row, write the coefficient in each column 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.

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