We are given the following expression
[tex]20+4(x+3y)-4x-8y-12+x_{}[/tex]
We are asked to identify the properties that were used to simplify the expression.
First of all, the distributive property of multiplication has been used
[tex]4(x+3y)=4x+12y\text{ }\mleft\lbrace a(b+c)=ab+ac\}\mright?[/tex]
Next, combine the like terms property has been used
[tex]\begin{gathered} 20-12+4x-4x+x+12y-8y_{} \\ (20-12)+(4x-4x+x)+(12y-8y) \end{gathered}[/tex]
Next, we have performed simple addition and subtraction so that the expression is reduced to
[tex]8+x+(12y-8y)_{}[/tex]
Then, we again used the distributive property of multiplication
[tex]12y-8y=y(12-8)\text{ }\mleft\lbrace ab-ac=a(b-c)\}\mright?[/tex]
Finally, the simplified expression is
[tex]8+x+4y[/tex]
Question 2:
The following statements are equivalent because of Associative Property of Addition
[tex]\begin{gathered} x+(y+9)=(x+y)+9_{}_{} \\ a+(b+c)=(a+b)+c_{} \end{gathered}[/tex]
Question 3:
Using the Commutative property we can write
[tex]\begin{gathered} 4\cdot a\cdot b \\ 4\cdot b\cdot a \\ a\cdot4\cdot b \end{gathered}[/tex]
As per the commutative property, the order doesn't matter.
The result of multiplication will be the same
