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

1 Answer
Jim H
Oct 2, 2015

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#

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