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7.1 Pascal’s Triangle and Binomial Theorem

7.1 Pascal’s Triangle and Binomial Theorem. 3/18/2013. Review. What if you have to figure out Wouldn’t that take FOREVER?!!. Pascal’s Triangle. What do you noticed about the coefficients of each term?. Pascal’s Triangle.

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7.1 Pascal’s Triangle and Binomial Theorem

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

  2. Review What if you have to figure out Wouldn’t that take FOREVER?!!

  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 nth power.

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

  6. Example: Use Pascal’s Triangle to write the binomial expansion of (x+2)6. (a + b)n 1. Make n + 1 columns (7 columns) 2. From the Pascal’s Triangle, 6th row, write the coefficient in each column. 3. Multiply each coefficient by x starting from x6, decreasing n by 1 in the next column until you reach x in the 2nd to the last column. 4. Starting in column 2, multiply each column by 2 increasing its exponent by 1 in the next column until you reach 26 in the last column. 1 2 3 4 5 6 7 1 6 15 20 15 6 1 5. Simplify.

  7. Example: Use Pascal’s Triangle to write the binomial expansion of (2y-3)4. (a + b)n 1. Make n + 1 columns (5 columns) 2. From the Pascal’s Triangle, 4th row, write the coefficient in each column. 3. Multiply each coefficient by 2y starting from (2y)4, decreasing n by 1 in the next column until you reach 2y in the 2nd to the last column. 4. Starting in column 2, multiply each column by -3 increasing its exponent by 1 in the next column until you reach -34in the last column. 1 2 3 4 5 1 4 6 4 1 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.”

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