# The simplified value of the expression ( x + y + z ) ( x − y − z ) . ### 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 60E
To determine

## To calculate: The simplified value of the expression (x+y+z)(x−y−z) .

Expert Solution

The value of the expression (x+y+z)(xyz) is x2y2z22yz .

### Explanation of Solution

Given information:

The expression (x+y+z)(xyz) .

Formula used:

To multiply two polynomial expressions, first multiply each term of first polynomial by second polynomial and then add the results. This property is known as distributive property, which is mathematically expressed as,

(a+b)(c+d)=a(c+d)+b(c+d)

Calculation:

Consider the given expression (x+y+z)(xyz) .

Recall the to multiply two polynomial expressions, first multiply each term of first polynomial by second polynomial and then add the results. This property is known as distributive property, which is mathematically expressed as,

(a+b)(c+d)=a(c+d)+b(c+d)

Apply it,

(x+y+z)(xyz)=x(xyz)+y(xyz)+z(xyz)=xx+x(y)+x(z)+yx+y(y)+y(z)+zx+z(y)+z(z)=x2xyxz+xyy2yz+zxzyz2

Combine the like terms and simplify it further as,

(x+y+z)(xyz)=x2xyxz+xyy2yz+zxzyz2=x2y2z2+(xyxy)+(zxzx)+(yzzy)=x2y2z22yz

Thus, the value of the expression (x+y+z)(xyz) is x2y2z22yz .

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