Question

Use the Binomial Theorem to find the binomial expansion of the expression. (s-5v)^5

Answer 1

s⁵+15s⁴v+90s³v²+270s²v³+405sv⁴+243v⁵

for me it was option b. not sure what is it for you.

I just took the test and that is what mine told me it was.

Answer 2

The solution would be like this for this specific problem:

C(5,0) = 5!/(0!×5!) = 1
C(5,1) = 5!/(1!×4!) = 5
C(5,2) = 5!/(2!×3!) = 10
C(5,3) = 5!/(3!×2!) = 10
C(5,4) = 5!/(4!×1!) = 5
C(5,5) = 5!/(5!×0!) = 1

(s−5v)⁵ = 1s⁵(−5v)⁰ + 5s⁴(−5v)¹ + 10s³(−5v)² + 10s²(−5v)³ + 5s¹(−5v)⁴ + 1s⁰(−5v)⁵
(s−5v)⁵ = s⁵ − 25s⁴v+ 250s³v² − 1250s²v³ + 3125sv⁴ − 3125

If you have any further questions, please don’t hesitate to ask again.