f(x)=(x-5)^5

Question

use either the binomial theorm or pascal's triangle

Answer 1

(x-5)⁵=[x+(-5)]⁵=

 

x⁵+5x⁴(-5)+10x³(-5)²+10x²(-5)³+5x(-5)⁴+(-5)⁵

Can you finish from here ?

Answer 2

Emma, sorry it's taken so long. If we use the binomial theorem, then we start with a^10 and go down to a^0 and do the opposite with the b's.

 

So, we have a^10b^0 + a^9b^1 + a^8b^2, etc...

 

For the coefficients, I used pascal's triangle. Let's see if I can type it.

 

        1           (0)

     1     1       (1)

  1    2     1     (2)

 1  3    3    1    (3)

1  4  6    4   1  (4)

 

If I carry this down to 10, then my final answer is:

 

a^10 + 10a^9b + 45a^8b^2 + 120a^7b^3 + 210a^6b^4 + 252a^5b^5 + 210a^4b^6 + 120a^3b^7 + 45a^2b^8 + 10ab^9 + b^10