# The simplified value of the expression x 1 4 ( 2 x 3 4 − x 1 4 ) .

### 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 52E
To determine

## To calculate: The simplified value of the expression x14(2x34−x14) .

Expert Solution

The value of the expression x14(2x34x14) is 2xx .

### Explanation of Solution

Given information:

The expression x14(2x34x14) .

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 x14(2x34x14) .

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,

x14(2x34x14)=x142x34x14x14

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,

x14(2x34x14)=2x14+34x14+14=2x44x24=2xx12=2xx

Thus, the value of the expression x14(2x34x14) is 2xx .

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