   # For Problems 7-20, expand and simplify. ( x − 3 y ) 5 ### Intermediate Algebra

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

#### Solutions

Chapter
Section ### Intermediate Algebra

10th Edition
Jerome E. Kaufmann + 1 other
Publisher: Cengage Learning
ISBN: 9781285195728
Chapter A, Problem 11PE
Textbook Problem
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## For Problems 7-20, expand and simplify. ( x − 3 y ) 5

To determine

To expand:

(x3y)5.

### Explanation of Solution

Let y=3y.

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.

Therefore,

(x3y)5=x5+5x4(3y)+542!x3(3y)2+5433!x2(3y)3+54324!x(3y)4+(3y)5

Here,

2!=213!=3214!=4321<

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