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 58E
To determine

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

Expert Solution

Answer to Problem 58E

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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