Question

How do you use pascals triangle to expand `(x-5)^6`?

Answer 1

`x^6-30x^5+375x^4-2500x^3+9375x^2-18750x+15625`

Explanation:

Since the binomial is taken to the 6th power we need the 6th row of Pascal's triangle. This is:

`1 - 6 - 15 - 20 - 15 - 6 - 1`

These are the co-effiecents for the terms of the expansion, giving us:

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

This evaluates to:
`x^6-30x^5+375x^4-2500x^3+9375x^2-18750x+15625`