# The factors of the expression a 3 − b 6 .

### 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 78E
To determine

## To calculate: The factors of the expression a3−b6 .

Expert Solution

The factors of the expression a3b6 are (ab2) and (a2+ab2+b4) .

### Explanation of Solution

Given information:

The expression a3b6 .

Formula used:

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

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

Calculation:

Consider the given expression a3b6 .

Rewrite it as,

a3b6=(a)3(b2)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=a and Y=b2 .

a3b6=(a)3(b2)3=(ab2)((a)2+(a)(b2)+(b2)2)=(ab2)(a2+ab2+b4)

Thus, the factors of expression a3b6 are (ab2) and (a2+ab2+b4) .

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