# Simplify form of the expression, 1 − x 2 x 3 − 1 ### 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 1.4, Problem 22E
To determine

## To calculate: Simplify form of the expression, 1−x2x3−1

Expert Solution

The value of the expression is, 1(1+x)x2+x+1

### Explanation of Solution

Given information:

The expression is given as: 1x2x31

Formula used:

The algebraic identity:

a2b2=(ab)(a+b) , a3b3=(ab)(a2+a+1)

Calculation:

Consider the equation

1x2x31

The expression is as, a2+b2a3b3=(a+b)(ab)(ab)(a2+b+1)

Therefore, the given equation is, 1x2x31

Apply the algebraic identity, a2+b2a3b3=(a+b)(ab)(ab)(a2+b+1)

,

Rewrite the expression:

1x2x31=(12)(x2)(x1)(x2+x+1)=(1+x)(1x)(x1)(x2+x+1)=(1+x)(x1)(x1)(x2+x+1)=(1+x)(x2+x+1)

The above expression can’t be simplified further.

Thus, the given expression is: 1(1+x)x2+x+1

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