Lesson 62- The Binomial Theorem

Expand and simplify each of the following powers of the binomial a + b:
(a + b)^1 = 1a + b^1
(a + b)^2 = 1a^2 + 2ab + 1b^2

Powers of a: decreasing
Powers of b: increasing

Example 1: (2x + 1)^4
= 4C0 (2x)^4(1)^0 + 4C1 (2x)^3 (1)^1 + 4C2 (2x)^2 (1)^2 + 4C3 (2x)^1(1)^3 + 4C4 (2x)^0 (1)^4
=  16x^4 + 32x^3 + 24x^2 + 8x + 1

Binomial Throrem using combinations:
( a + b)^n = nC0 (a)^n (b)^0