Question

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

Answer 1

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

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