Posted by Jonathan on Monday, December 5, 2011 at 9:35am.
you know the expansion must look like
?x^5(-1)^0 + ?x^4(-1)^1 + ?x^3(-1)^2 + ?x^2(-1)^3 + ?x^1(-1)^4 + ?x^0(-1)^5
= ?x^5 - ?x^4 + ?x^3 - ?x^2 + ?x - ?
now the 5th row of the triangle has values:
1 5 10 10 5 1
put these in where the ?'s are and you are done
= x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1
suppose you had
(x+2)^4
= 1x^4 + 4x^3(2) + 6x^2(2^2) + 4x(2^3) + 12^4
= x^4 + 8x^3 + 24x^2 + 32x + 16
That last term in the 2nd last row of course is 1(2^4) or 16
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