Question

Expand the following using either the Binomial Theorem or Pascal’s Triangle. You must show your work for credit.

(x - 5)^5

Answer 1

do you know what pascals triangle is?

Answer 2

Yes

Answer 3

I realize that I have to go to the fifth row, but don't understand what to do afterwards

Answer 4

1 5 10 10 5 1

Answer 5

Right! So pascals triangle essentially gives you the coefficients for an expanded perfect power polynomial

So really quickly its:
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

Answer 6

Okay, I get that

Answer 7

Hello?

Answer 8

@LifeEngineer

Answer 9

forgot a row btw... should be 1, 11, 121...***

so for example, a perfect cube such as (a+b)^3 could be expanded using the fourth row (the first row is for the zeroth power) of pascals triangle

(a+b)^3 = 1*a^3 + 3*a^2*b + 3*a*b^2 + 1*b^3

Answer 10

where pascals triangle gives you the coefficients on each term, and you increment the power on the 'a' term, and decrement the power on the 'b' term

Answer 11

this makes things a good bit easier than actually expanding the whole term

Answer 12

You said that the coefficients are used for Pascals triangle

Answer 13

now in your case, you have (x-5)^5, so you'd need to use the 6th row of pascals triangle (1 5 10 10 5 1) to get the coefficients of each term, then go through and add your a's and b's (in this case x and -5) to the appropriate powers

start with x^5*(-5)^0 which is your highest degree term. the first number in pascals triangle for the 6th row is 1 so you get 1*x^5

then the second term would be x^4 * (-5)^1, with a coefficient of 5
this gives you 5*(x^4)*(-5) = -25x^4

continuing on with the third term ( x^3*(-5)^2 ), the coefficient is 10 so your term would be
10*(x^3)*(-5)^2

and so on and so forth until all your terms are satisfied! I hope that helped, I realize my explanation wasnt the best...