What is the coefficient of the x5y5-term in the binomial expansion of (2x – 3y)10?

In mathematics, the coefficient of a term in an infinite series is a measure of how important that term is. This article will show you how to find the coefficient of a binomial expansion, and it will also provide some tips on how to use the binomial theorem.

Background

The coefficient of the xy-term in the binomial expansion of (x – y) is known as the Gini coefficient. This coefficient measures the inequality between the incomes of people in a given population.

The Gini coefficient can be thought of as the logarithm of the percentage of income earned by people in a given population. For example, if 50% of the population earns more than $50,000 and 50% earns less than $50,000, then their Gini coefficient would be 0.50. In contrast, if all of the people in a population earn exactly $50,000, their Gini coefficient would be 1.00.

The Gini coefficient is widely used to measure inequality in populations. It is often used to measure the distribution of income among different groups of people. For example, it can be used to measure how well different sections of society are doing economically.

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The Solution

The coefficient of the xy-term in the binomial expansion of (x – y) is given by:

Coefficient = (n*(2*x+1))/(n*(2*y+1))

Conclusion

The coefficient of the x5y5-term in the binomial expansion of (2x – 3y)10 is 1.

FAQ

The coefficient of the xy-term in the binomial expansion of (x – y) can be found using the quadratic Formula. The quadratic Formula states that the coefficient of a term in the binomial expansion of (x – y) is equal to the square of the second term minus the square of the first term. In other words, it is:

Coefficient of xy-term = (2x – y)(x – y2)

To find the coefficient of the xy-term, we need to find both terms in parentheses. We can do this by multiplying each term in parentheses by itself and dividing the result by 2. The result is:

(2x – y)(x – y2) = (4x – 16y)(x – 8y2)

which gives us:

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Coefficient of xy-term = 4x – 16y

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