Summary Binomial Expansion

Using Binomial Expansion
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The binomial theorem

Pascal’s Tringle

(a + b)^n
(a + b)^0 = 1
(a + b)^1 = a + b
(a + b)^2 = a^2 + 2ab + b^2
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3




Example:
Expand (1 – 3x)^4 using binomial theorem

(a + b)^4 = (4)a^4 + (4)a^3b + (4)a^2b^2 + (4)ab^3 + (4)b^4
(0) (1) (2) (3) (4)

= 1 4 6 4 1

(1 – 3x)^4 = 1 – 12x + 54x^2 + 108x^3 + 108x^4


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nCr = n!/r!(n – r)! 0^1 = 1

Example:
5!/2!(5 - 2!) = 5!/2!3! = 5 x 4 x 3/2 x 3 = 10