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

BuyFind

### Precalculus: Mathematics for Calcu...

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

### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 1.3, Problem 57E
To determine

Expert Solution

## Answer to Problem 57E

The value of the expression ((x1)+x2)((x1)x2) is x4+x22x+1 .

### Explanation of Solution

Given information:

The expression ((x1)+x2)((x1)x2) .

Formula used:

The special product formula of difference of squares to multiply the algebraic expressions is mathematically expressed as,

(A+B)(AB)=A2B2

Special product of formula of perfect square of algebraic expressions which can be mathematically expressed as,

(AB)2=A22AB+B2

Calculation:

Consider the given expression ((x1)+x2)((x1)x2) .

Recall the special product formula of difference of squares to multiply the algebraic expressions is mathematically expressed as,

(A+B)(AB)=A2B2

Here, A=x1 and B=x2 .

Apply it,

((x1)+x2)((x1)x2)=(x1)2(x2)2

Now, recall the special product of formula of perfect square of algebraic expressions which can be mathematically expressed as,

(AB)2=A22AB+B2

((x1)+x2)((x1)x2)=(x1)2(x2)2=x22(x)(1)+12x4=x4+x22x+1

Thus, the value of the expression ((x1)+x2)((x1)x2) is x4+x22x+1 .

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