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

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Answer 1 · 2015-08-17T21:28:14

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

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

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