Posted by Jonathan on .
I need to use Pascal's Triangle to expand (x1)^5
I know I use the fifth row but I'm not sure how to do it I have a bunch of these and I'm really confused Please help if you can

Algebra 
Reiny,
Monday, December 5, 2011 at 10:31am
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 
Algebra 
Reiny,
Monday, December 5, 2011 at 10:33am
That last term in the 2nd last row of course is 1(2^4) or 16