a(b+c)=a* b+a* c.We want to verify whether or not the given equation demonstrates the Distributive Property.
-2(x+1)=-2x-2
We can do that by distributing -2 on the left-hand side to the terms inside the parentheses. Then we will compare the obtained result to the right-hand side of the equation.
Since the left-hand side now matches the given right-hand side, we know that the Distributive Property was shown.
b Consider the given equation.
(s-4)8=8(s-4)
This equation demonstrates the Commutative Property of Multiplication which shows that the factors of a product can be rearranged without changing the product's value.
a* b&= b* a
(s-4) 8&= 8 (s-4)
Note, the 8 was not distributed to the terms inside the parentheses. Therefore, we did not use the Distributive Property.
c Consider the given equation.
5n-45=5(n-9)This equation demonstrates factoring out a common factor.
Note that if we rearrange the equation, we will get a perfect example of the use of the Distributive Property.
5n-45=5(n-9)
⇕
5(n-9)=5n-45
Therefore, the given equation demonstrates the Distributive Property but in the opposite direction.
d Consider the given equation.
8+(t+6)=(8+t)+6
This equation demonstrates the Associative Property of Addition which shows that we can add terms in different orders without changing the sum.
a+ ( b+ c)&=( a+ b)+ c
8+ ( t+ 6)&=( 8+ t)+ 6
In the equation does not occur any distribution, so it does not demonstrate the Distributive Property.
