9.5 Binomial Theorem

(a+b)^0 = 1

(a+b)^1 = a+b

(a+b)^2 = a^2 +2ab+b^2

etc.

Binomials raised to a power that is a natural number follow the pattern of pascals triangle.

*The coefficients of the terms of the binomial (a+b)^n are the terms of pascals triangle in row "n" as they appear from left to right.

*The power that "a" is raised to starts at "n" and decreases by 1 each term until it reaches 0

*The power that "b" is raised to starts at 0 and increases by 1 until it reaches "n"

example: (a+b)^2

the terms of row 2 of pascals triangle are 1, 2, 1

(a+b)^2 = (1)a^2 + (2)ab + (1)b^2

= a^2 + 2ab + b^2