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Expand using the Binomial Theorem (3x+2)^4
(3x+2)4(3x+2)4
Use the binomial expansion theorem to find each term. The binomial theorem states (a+b)n=n∑k=0nCk⋅(an−kbk)(a+b)n=∑k=0nnCk⋅(an-kbk).
4∑k=04!(4−k)!k!⋅(3x)4−k⋅(2)k∑k=044!(4-k)!k!⋅(3x)4-k⋅(2)k
Expand the summation.
4!(4−0)!0!⋅(3x)4−0⋅(2)0+4!(4−1)!1!⋅(3x)4−1⋅(2)+4!(4−2)!2!⋅(3x)4−2⋅(2)2+4!(4−3)!3!⋅(3x)4−3⋅(2)3+4!(4−4)!4!⋅(3x)4−4⋅(2)44!(4-0)!0!⋅(3x)4-0⋅(2)0+4!(4-1)!1!⋅(3x)4-1⋅(2)+4!(4-2)!2!⋅(3x)4-2⋅(2)2+4!(4-3)!3!⋅(3x)4-3⋅(2)3+4!(4-4)!4!⋅(3x)4-4⋅(2)4
Simplify the exponents for each term of the expansion.
1⋅(3x)4⋅(2)0+4
Hope this helps!
I'm pretty sure that it would be 1/2 since it says 1/3 each whole, which in this case it would be 1/3 each hour.
