# The simplified value of the expression y 1 3 ( y 2 3 + y 5 3 ) .

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.3, Problem 51E
To determine

## To calculate: The simplified value of the expression y13(y23+y53) .

Expert Solution

The value of the expression y13(y23+y53) is y2+y .

### Explanation of Solution

Given information:

The expression y13(y23+y53) .

Formula used:

To multiply two polynomial expressions, first multiply each term of first polynomial by second polynomial and then add the results. This property is known as distributive property, which is mathematically expressed as,

Law of exponent which states that to find the product of two terms with same base and different exponents, then add the exponents only keeping the base same, which can be written mathematically as,

xmxn=xm+n

Calculation:

Consider the given expression y13(y23+y53) .

Recall that to multiply two polynomial expressions, first multiply each term of first polynomial by second polynomial and then add the results. This property is known as distributive property, which is mathematically expressed as,

Apply it,

y13(y23+y53)=y13y23+y13y53

Recall the law of exponent which states that to find the product of two terms with same base and different exponents, then add the exponents only keeping the base same, which can be written mathematically as,

xmxn=xm+n

Apply it,

y13(y23+y53)=y13y23+y13y53=y13+23+y13+53=y33+y63=y+y2

Thus, the value of the expression y13(y23+y53) is y2+y .

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