# The simplified value of the expression ( 1 − 2 r ) 3 . ### 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 43E
To determine

## To calculate: The simplified value of the expression (1−2r)3 .

Expert Solution

The value of the expression (12r)3 is 8r3+12r26r+1 .

### Explanation of Solution

Given information:

The expression (12r)3 .

Formula used:

The special product formula of perfect cube to multiply the algebraic expressions is mathematically expressed as,

(AB)3=A33AB(AB)B3

Calculation:

Consider the given expression (12r)3 .

Recall the special product formula of perfect cube to multiply the algebraic expressions is mathematically expressed as,

(AB)3=A33AB(AB)B3

Apply it,

(12r)3=(1)33(1)(2r)(12r)(2r)3=16r(12r)8r3=16r+12r28r3=8r3+12r26r+1

Thus, the value of the expression (12r)3 is 8r3+12r26r+1 .

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