Pascal's Triangle and Binomial Theorem

​Pascal's Triangle

​•Pascal’s triangle help to determine all coefficients of a binomial expansion. Where a, b ∈ R, and exponent n ∈ N

​Start with number “1” at the top, then continue placing numbers below by the sum of two consecutive numbers on the same row.

​Pascal's Triangle

​•Pascal’s triangle help to determine all coefficients of a binomial expansion. Where a, b ∈ R, and exponent n ∈ N

​Start with number “1” at the top, then continue placing numbers below by the sum of two consecutive numbers on the same row.

​Pascal's Triangle

​•Pascal’s triangle help to determine all coefficients of a binomial expansion. Where a, b ∈ R, and exponent n ∈ N

​Start with number “1” at the top, then continue placing numbers below by the sum of two consecutive numbers on the same row.

​Binomial Expansion

​•Use Pascal’s triangle to determine the coefficients. The number terms of the expansion are n + 1

•1st variable’s degree from the given n will reduce 1 less from the left to right.

•2nd variable’s degree from the given n will reduce 1 less from the right to left.

•For a negative case (a-b)ⁿ case the sign will be alternative operation for each term beginning with positive then negative sign.

​(a + b)ⁿ =

​Ex1: (a + b)²

​(a + b)² =

Ex2: ​(a + b)³

​(a + b)³ =

​Ex4: (a − b)⁴

​(a − b)⁴ =

​(ax + by)⁵

​(ax + by)⁵ =

​(a − b)³

​(a − b)³ =

​(a + b)⁴

​(a + b)⁴ =