# The factors of the expression 8 x 3 − 125 .

### 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 113E
To determine

## To calculate: The factors of the expression 8x3−125 .

Expert Solution

The factors of the expression 8x3125 are (2x5) and (4x2+10x+25) .

### Explanation of Solution

Given information:

The expression 8x3125 .

Formula used:

The special factoring formula of difference of cubes which is expressed as,

X3Y3=(XY)(X2+XY+Y2)

Calculation:

Consider the given expression 8x3125 .

Rewrite it as,

8x3125=(2x)3(5)3

Recall the special factoring formula of difference of cubes which is expressed as,

X3Y3=(XY)(X2+XY+Y2)

Here, the values of X and Y are X=2x and Y=5 .

8x3125=(2x)3(5)3=(2x5)((2x)2+(2x)(5)+(5)2)=(2x5)(4x2+10x+25)

Thus, the factors of expression 8x3125 are (2x5) and (4x2+10x+25) .

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