How do you expand (d-4)^6(d−4)6 using Pascal’s Triangle?

1 Answer
P dilip_k
May 13, 2016

as follws

Explanation:

The power of the given binomial expression (d-4)^6(d−4)6 is 6

  • Generate a Pascal's triangle of 6+1=7 rows as follows
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  • The numbers of last row i.e (1,6,15,20,15,6,1) are to be taken as coefficients of the terms starting from first one with alternative plus ('+') and minus ( '-') sign as there exist a minus sign between two terms in the given expression.
  • The power first term d will decrease by unity from 6 and will end at zero.
  • The power of 2nd term 4 will increase by unity from zero and will end at 6

Hence the expansion becomes
(d-4)^6=1*d^6*4^0-6*d^5*4^1+15*d^4*4^2-20*d^3*4^3 +15*d^2*4^4-6*d^1*4^5+1*d^0*4^6(d−4)6=1⋅d6⋅40−6⋅d5⋅41+15⋅d4⋅42−20⋅d3⋅43+15⋅d2⋅44−6⋅d1⋅45+1⋅d0⋅46

=d^6-24d^5+240d^4-1280d^3+3840d^2-6144d+4096=d6−24d5+240d4−1280d3+3840d2−6144d+4096

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