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What is the coefficient of x³y² in the expansion of (2x+y)5?

O A 2
OB. 5
OC. 40
OD. 80
OE. It does not exist.
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1 Answer

3 votes

Answer:

D. 80

Explanation:

You want the coefficient of the x³y² term in the expansion of the binomial (2x +y)⁵.

Binomial expansion

The k-th term in the expansion of the binomial (a +b)^n will be given by ...

(nCk)(a^(n-k))(b^k) . . . . . . . where k = 0 .. n, and nCk = n!/(k!(n-k)!)

We want the term for a = 2x, b = y, n = 5, k = 2:

(5C2)(2x)³)(y²) = 10·8x³y² = 80x³y²

The coefficient of the term of interest is 80, matching choice D.

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What is the coefficient of x³y² in the expansion of (2x+y)5? O A 2 OB. 5 OC. 40 OD-example-1
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