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What is the coefficient of the x^5y^5 term in the binomial expansion of (2x-3y)^10?

What is the coefficient of the x^5y^5 term in the binomial expansion of (2x-3y)^10?-example-1
User Plutownium
by
7.4k points

2 Answers

5 votes

Answer:

second one

Explanation:

User Prateek Thapa
by
7.6k points
1 vote

ANSWER


10C_5(2)^(5)( - 3)^5

EXPLANATION

The given binomial expression is


(2x-3y)^(10)

The nth term in this expansion is calculated using the formula,


T_(r+1) = nC_ra^(n-r)b^r

To find the term with coefficient


{x}^(5) {y}^(5)

we substitute r=5, n=10, a=2x, and b=-3y


T_(6) = 10C_5(2x)^(10-5)( - 3y)^5


T_(6) = 10C_5(2x)^(5)( - 3y)^5


T_(6) = 10C_5(2)^(5)( - 3)^5 {x}^(5) {y}^(5)

The coefficient is


10C_5(2)^(5)( - 3)^5

The second choice is correct.

User Shar
by
8.3k points

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