# The factor of the expression r 2 − 6 r s + 9 s 2 .

### 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 108E
To determine

## To calculate: The factor of the expression r2−6rs+9s2 .

Expert Solution

The factor of the expression r26rs+9s2 is (r3s)2 .

### Explanation of Solution

Given information:

The expression r26rs+9s2 .

Formula used:

The special factoring formula of perfect square which is expressed as,

X22XY+Y2=(XY)2

Calculation:

Consider the given expression r26rs+9s2 .

Rewrite it as,

r26rs+9s2=(r)22(r)(3s)+(3s)2

Recall the special factoring formula of perfect square which is expressed as,

X22XY+Y2=(XY)2

Here, the values of X and Y are X=r and Y=3s .

r26rs+9s2=(r)22(r)(3s)+(3s)2=(r3s)2

Thus, the factor of expression r26rs+9s2 is (r3s)2 .

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