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

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Answer 1 · 2015-10-02T17:54:24

See the explanation below.

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 $6$ .

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

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

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

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