1) factor the denominators: 2b/(b-1)2 - 2/ (b-1)2
2) MAKE SURE YOU HAVE A COMMON DENOMINATOR
3) combine the numerators: 2b-2/(b-1)2
4) distribute 2 from numerator: 2(b-1)/(b-1)2
5) simplify; answer is 2/(b-1)
The third term of the expansion is 6a^2b^2
<h3>How to determine the third term of the
expansion?</h3>
The binomial term is given as
(a - b)^4
The r-th term of the expansion is calculated using
r-th term = C(n, r - 1) * x^(n - r + 1) * y^(r - 1)
So, we have
3rd term = C(4, 3 - 1) * (a)^(4 - 3 + 1) * (-b)^(3-1)
Evaluate the sum and the difference
3rd term = C(4, 2) * (a)^2 * (-b)^2
Evaluate the exponents
3rd term = C(4, 2) * a^2b^2
Evaluate the combination expression
3rd term = 6 * a^2b^2
Evaluate the product
3rd term = 6a^2b^2
Hence, the third term of the expansion is 6a^2b^2
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Using the Instant-runoff method, it can be inferred that the winner is the tacos because after the first vote, they get 3 more votes that allow them to have more than half of the possible votes (option B).
<h3>What is the instant-runoff method?</h3>
Instant-runnof is a voting method whereby a single winner is selected from a wide variety of options. This method is characterized by allowing voters to choose different options on a scale of first option, second option, third option.
According to the above, in the first vote the sandwiches are eliminated because they had the lowest vote (3 votes). Then, a new vote must be carried out with the products that were left that were Pizza and Tacos.
On the second ballot, tacos get 3 more votes because voters who voted for Sandwich on the first ballot had Tacos as their second choice. So the bottom line is Pizza with 9 votes and Tacos with 11 votes.
In short, the Tacos win by having more than half of the possible votes 11/20.
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