# For Problems 25-30, find the indicated term of the expansion. Third term of ( 2 x − 5 y ) 5

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728

Chapter
Section

### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter A, Problem 29PE
Textbook Problem
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## For Problems 25-30, find the indicated term of the expansion.Third term of ( 2 x − 5 y ) 5

To determine

To Find:

The third term of the expansion (2x5y)5.

### Explanation of Solution

Let x=2xandy=5y.

The binomial expansion for (x+y)n is

xn+nxn1y+n(n1)2!.xn2y2+n(n1)(n2)3!xn3y3+........+yn

The exponents of x begin with the exponent of 5 and decrease term by term by 1 until the last term becomes 1, i.e. the exponent of x is 0.

The exponents of y begin with 0 and increase term by term by 1 until the last term contains the power of 5.

But, here we need to find the third term of the expansion.

The third term will contain x3 and y2

Because the sum of the exponents of xandy must be 5

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