# The factors of the expression 8 s 3 − 125 t 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 79E
To determine

## To calculate: The factors of the expression 8s3−125t3 .

Expert Solution

The factors of the expression 8s3125t3 are (2s5t) and (4s2+10st+25t2) .

### Explanation of Solution

Given information:

The expression 8s3125t3 .

Formula used:

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

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

Calculation:

Consider the given expression 8s3125t3 .

Rewrite it as,

8s3125t3=(2s)3(5t)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=2s and Y=5t .

8s3125t3=(2s)3(5t)3=(2s5t)((2s)2+(2s)(5t)+(5t)2)=(2s5t)(4s2+10st+25t2)

Thus, the factors of expression 8s3125t3 are (2s5t) and (4s2+10st+25t2) .

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