Question

I need to use Pascal's Triangle to expand (x-1)^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-

Answer 1

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
= <b>1</b>x^4 + <b>4</b>x^3(2) + <b>6</b>x^2(2^2) + <b>4</b>x(2^3) + <b>1</b>2^4
= x^4 + 8x^3 + 24x^2 + 32x + 16

Answer 2

That last term in the 2nd last row of course is 1(2^4) or 16