   # For Problems 7-20, expand and simplify. ( x + y 3 ) 6 ### 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 15PE
Textbook Problem
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## For Problems 7-20, expand and simplify. ( x + y 3 ) 6

To determine

To expand:

(x+y3)6.

### Explanation of Solution

Let y=y3

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 6 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 6.

Therefore,

(x+y3)6=x6+6x5(y3)+652!x4(y3)2+6543!x3(y3)3+65434!x2(y3)4+654325!x(y3)5+(y3)6

Here,

2!=213!=3214!=43215!=543216!=6543

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