# The factors of the expression 27 x 3 + y 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 77E
To determine

## To calculate: The factors of the expression 27x3+y3 .

Expert Solution

The factors of the expression 27x3+y3 are (3x+y) and (9x23xy+y2) .

### Explanation of Solution

Given information:

The expression 27x3+y3 .

Formula used:

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

X3+Y3=(X+Y)(X2XY+Y2)

Calculation:

Consider the given expression 27x3+y3 .

Rewrite it as,

27x3+y3=(3x)3+(y)3

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

X3+Y3=(X+Y)(X2XY+Y2)

Here, the values of X and Y are X=3x and Y=y .

27x3+y3=(3x)3+(y)3=(3x+y)((3x)2(3x)(y)+(y)2)=(3x+y)(9x23xy+y2)

Thus, the factors of expression 27x3+y3 are (3x+y) and (9x23xy+y2) .

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