# Thesimplified form of the expression x 3 x + 1 x x 2 + 2 x + 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 35E
To determine

## To calculate: Thesimplified form of the expression x3x+1xx2+2x+1 .

Expert Solution

The simplified form of the expression is x3+x2 .

### Explanation of Solution

Given information:

The expression is x3x+1xx2+2x+1 .

Formula used:

If a, b, c and d are any numbers then abcd is expressed by a×bc×d .

The sum of the square of two numbers is algebraically expressed as (a+b)2=a2+b2+2ab .

Calculation:

Consider the provided expression x3x+1xx2+2x+1 .

Recall that if a, b, c and d are any numbers then abcd is expressed by a×bc×d . Apply it in the above expression.

x3x+1xx2+2x+1=x3×(x2+2x+1)(x+1)×x

Recall that the sum of the square of two numbers is algebraically expressed as (a+b)2=a2+b2+2ab . Apply it,

x3x+1xx2+2x+1=x3×(x2+2x+1)(x+1)×x  =xx2x((x2+2×x×1+12))(x+1)=x2×(x+1)2(x+1)

Strike off the common terms,

x3x+1xx2+2x+1=x2×(x+1)2(x+1)=x2×(x+1)(x+1)(x+1)=x2(x+1)

Expand the expression obtained above,

x3x+1xx2+2x+1=x2×(x+1)2(x+1)=x2×(x+1)(x+1)(x+1)=x2(x+1)=x3+x2

Thus, the simplified form of the expression is x3+x2 .

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