# The simplified value of the expression ( x + ( 2 + x 2 ) ) ( x − ( 2 + x 2 ) ) . ### 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 58E
To determine

## To calculate: The simplified value of the expression (x+(2+x2))(x−(2+x2)) .

Expert Solution

The value of the expression (x+(2+x2))(x(2+x2)) is x43x24 .

### Explanation of Solution

Given information:

The expression (x+(2+x2))(x(2+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,

(A+B)2=A2+2AB+B2

Calculation:

Consider the given expression (x+(2+x2))(x(2+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=x and B=2+x2 .

Apply it,

(x+(2+x2))(x(2+x2))=(x)2(2+x2)2

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

(A+B)2=A2+2AB+B2

Apply it to solve the expression (2+x2)2 ,

(x+(2+x2))(x(2+x2))=x2(2+x2)2=x2(22+2(2)(x2)+(x2)2)=x2(4+4x2+x4)

Simplify it further as,

(x+(2+x2))(x(2+x2))=x2(4+4x2+x4)=x244x2x4=x43x24

Thus, the value of the expression (x+(2+x2))(x(2+x2)) is x43x24 .

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