Question

How do you find the binomial expansion of the expression `(d-5)^6`?

Answer 1

`d^6 +6d^5(-5)+ 15d^4 (-5)^2 +20 d^3 (-5)^3 + 15d^2 (-5)^4 +6d (-5)^5 + (-5)^6`

Explanation:

The binomial expansion can be written, symmetrical form
as follows( Think of the Pascal Triangle):

`d^6 + 6C_1 d^5 (-5)^1 + 6C_2 d^4 (-5)^2 + 6C_3 d^3 (-5)^3+ 6C_4 d^2 (-5)^4 + 6C_5 d (-5)^5 + 6C_6 (-5)^6`

Here `6C_1 =6; 6C_2 = (6*5)/(1*2)= 15; 6C_3 = (6*5*4)/ (1*2*3)=20; 6C_4 = 6C_2 = 15; 6C_5= 6C_1 =6, 6C_6 = 1`

`d^6 +6d^5(-5)+ 15d^4 (-5)^2 +20 d^3 (-5)^3 + 15d^2 (-5)^4 +6d (-5)^5 + (-5)^6`