# Explain how to find the fifth term of the expansion of ( 2 x + 3 y ) 9 without writing out the entire expansion.

### 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 32PE
Textbook Problem
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## Explain how to find the fifth term of the expansion of ( 2 x + 3 y ) 9 without writing out the entire expansion.

To determine

To find:

The fifth term of the expansion (2x+3y)9.

### Explanation of Solution

Let x=2xâ€Šâ€Šâ€Šâ€Šandâ€Šâ€Šâ€Šâ€Šâ€Šy=3y.

The exponents of x begin with the exponent of the binomial 9 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 the original binomial, i.e. 9.

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

The fifth term will contain x5 and y4

Because the sum of the exponents of xâ€Šâ€Šâ€Šandâ€Šâ€Šâ€Šâ€Šy must be 9.

Then, the numerator of the coefficient contains r factors, where the values of r agrees with the exponent of y for each term.

The denominators of the coefficients are of the form r!

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