SOLUTION: Use the Binomial Theorem to expand the binomial. (3v + s)5

Question 694383: Use the Binomial Theorem to expand the binomial.
(3v + s)5
Found 2 solutions by jim_thompson5910, mouk:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Look at Row 6 in Pascals triangle to see these numbers: 1, 5, 10, 10, 5, 1

These coefficients multiply with the following terms:

(3v)^5*(s)^0
(3v)^4*(s)^1
(3v)^3*(s)^2
(3v)^2*(s)^3
(3v)^1*(s)^4
(3v)^0*(s)^5

So multiply them to get the following

1*(3v)^5*(s)^0
5*(3v)^4*(s)^1
10*(3v)^3*(s)^2
10*(3v)^2*(s)^3
5*(3v)^1*(s)^4
1*(3v)^0*(s)^5

1*(243v^5)*(1)
5*(81v^4)*(s)
10*(27v^3)*(s^2)
10*(9v^2)*(s^3)
5*(3v)*(s^4)
1*(1)*(s^5)

243v^5
405sv^4
270s^2v^3
90s^3v^2
15s^4v
s^5

Then add up all the terms to get this final answer

243v^5 + 405sv^4 + 270s^2v^3 + 90s^3v^2 + 15s^4v + s^5

So

(3v+s)^5 = 243v^5 + 405sv^4 + 270s^2v^3 + 90s^3v^2 + 15s^4v + s^5

Answer by mouk(232) (Show Source): You can put this solution on YOUR website!

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