Name the property of real numbers illustated by the equation -4(x+4)=-4x-16

The given expression -4( x + 4 ) = -4 x - 16 illustrates the DISTRIBUTIVE PROPERTY

Step-by-step explanation:

DISTRIBUTIVE PROPERTY:

This property states that if we multiply a number with sum of two number, it is equivalent to multiplying the number separately with two numbers and adding them.

⇒ A ( B + C)  = A B  + A C

Here, -4( x + 4 ) = -4x - 16

Simplifying Left side with distributive property, we get

-4( x + 4 )   = -4(x)  + (-4)(4)

                  = -4x  - 16  =  Right Side

Hence, the given expression -4( x + 4 ) = -4 x - 16 illustrates the DISTRIBUTIVE PROPERTY

Answer:

The property of real numbers illustrated by the equation -4(x+4)=-4x-16 is distributive property of multiplication over addition.

Explanation:

Lets see distributive property of multiplication over addition.

Consider one example

5 x 110  

There are two ways of approaching to the solution

First way

5 x (100 + 10 ) = 5 x 110 = 550

Second way

(5 x 100 ) + ( 5 x 10 ) = 500 + 50 = 550

So we can say that 5 x (100 + 10 ) = (5 x 100 ) + ( 5 x 10 ) = 550

Lets replace 5 by any real number a , 100 by real number b and 10 by real number c.

So we get a x ( b + c ) = ( a x b + b x c )  

=> a(b+c ) = ab + bc

In our case a = -4 , b = x and c = 4 that is  

Hence we can conclude that the property of real numbers illustrated by the equation -4(x+4)=-4x-16 is distributive property of multiplication over addition.

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