The Binomial Theorem states that for any positive integer n, the expansion of the binomial (a + b)^n can be given by the following formula:
(a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n
In this case, the binomial is (s + 3v)^5.
By substituting a = s and b = 3v, we can apply the Binomial Theorem to expand the binomial:
(s + 3v)^5 = C(5, 0) * s^5 * (3v)^0 + C(5, 1) * s^4 * (3v)^1 + C(5, 2) * s^3 * (3v)^2 + C(5, 3) * s^2 * (3v)^3 + C(5, 4) * s^1 * (3v)^4 + C(5, 5) * s^0 * (3v)^5
Now, let's simplify each term:
= 1 * s^5 * 1 + 5 * s^4 * 3v + 10 * s^3 * (3v)^2 + 10 * s^2 * (3v)^3 + 5 * s^1 * (3v)^4 + 1 * s^0 * (3v)^5
= s^5 + 15s^4v + 90s^3v^2 + 270s^2v^3 + 405sv^4 + 243v^5
Therefore, the binomial (s + 3v)^5 expands to s^5 + 15s^4v + 90s^3v^2 + 270s^2v^3 + 405sv^4 + 243v^5.
Use the Binomial Theorem to expand the binomial.
left parenthesis s plus 3 v right parenthesis Superscript 5 baseline
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