7.7 pascal’s triangle & binomial expansion

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Presentation transcript:

7.7 pascal’s triangle & binomial expansion

Homefun  pg 466 # 1, 2ac, 4adf, 5abef, 8

Pascal’s triangle What is the pattern? Determine the next 5 rows.

Pascal’s triangle

PAScal’s triangle

PAScal’s triangle The triangular array of numbers . It originated in China about 1100 A.D. but Blaise Pascal developed and applied many of its properties in the 17th century. Each row of Pascal’s Triangle is symmetrical. An entry in any row can be determined by adding the numbers diagonally above it to the left and right.

Pascal’s triangle & BINOMIAL EXPANSION

Pascal’s triangle & BINOMIAL EXPANSION

EXAMPLE 1

EXAMPLE 1

EXAMPLE 2 – Expand & simplify

EXAMPLE 2 – Expand & simplify

EXAMPLE 3 – Expand & simplify

EXAMPLE 3 – Expand & simplify

EXAMPLE 4 Determine the values of a, b and n. (x + y)n = x10 + 10x9y + 45x8y2 + ax7y3 + … + 45x2yb + … + y10,

Example 5 As indicated in the diagram below, water is poured into the top dish and then overflows into the other dishes. How many different paths could a single drop of water follow in its journey from the top dish to the bottom row of dishes?

EXAMPLE 6 A six by six checkerboard is shown below with a checker already placed on the board. You are allowed to move one square diagonally up (left or right) at any one time. How many paths will take the checker from the bottom of the board to the top?

Homefun  pg 466 # 1, 2ac, 4adf, 5abef, 8