Question

How do you expand `(d - 5)^6` using Pascal’s Triangle?

Answer 1

See the explanation below.

Explanation:

Use the 7th row:
`1" "6" "15" "20" "15" "6" "1` to get the coefficients.

Powers on `d` are decreasing from `6` to `0` and powers on `-5` are increasing from `0` to `6`.

`(d-5)^6 = 1d^6+6d^5(-5)^1+15d^4(-5)^2+20d^3(-5)^3+15d^2(-5)^4+6d^1(-5)^5+1(-5)^6`

`=d^6+6d^5(-5)+15d^4(25)+20d^3(-125)+15d^2(625)+6d^1(-3125)+1(15 625)`

`= d^6-30d^5+375d^4-2500d^3+9375d^2-18750d+15 625`