# The property of the real numbers being used, ( A + 1 ) ( x + y ) = ( A + 1 ) x + ( A + 1 ) y . ### 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, Problem 4RE
To determine

## To describe: The property of the real numbers being used, (A+1)(x+y)=(A+1)x+(A+1)y .

Expert Solution

Distributive property of addition is used in the expression.

### Explanation of Solution

Given information:

The expression, 4(a+b)=4a+4b

The distributive property is a property in which, a(b+c)=ab+ac .it means when multiply numbers as, , a(b+c) then this number a multiplies to both the numbers ab+ac

It is like a constants is multiplyied to the sum of two numbers then the result is same , ab+ac

As when multiply a number to sum of to numbers. Then the numbers are same as would get if.

For example:

(4+1)(x+y)=(x+y)4+(x+y)15(x+y)=4x+4y+x+y5x+5y=5x+5y0=0

Apply the property , , a(b+c)=ab+ac

Rewrite the expression as,

(A+1)(x+y)=(A+1)x+(A+1)yAx+Ay+x+y=Ax+x+Ay+yAx+Ay+x+y=Ax+Ay+x+y0=0 .

The above expression is satisfied the distributive property.

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