We have been given 4 expressions. We are asked to choose the expressions, which simplifies to 0.
Let us check our given choices one by one.
1. [tex]8g-8g[/tex]
[tex]8(g-g)[/tex]
[tex]8(0)=0[/tex]
When we will subtract 8g from 8g, we will get 0. Therefore, expression [tex]8g-8g[/tex] simplifies to 0.
2. [tex](-2g)-2g[/tex]
Let us remove parenthesis.
[tex]-2g-2g[/tex]
Upon combining like terms, we will get:
[tex]-4g[/tex]
Since [tex](-2g)-2g[/tex] simplifies to [tex]-4g[/tex], therefore, expression [tex]-2g-2g[/tex] is not a correct choice.
3. [tex]5g+(-5g)[/tex]
Let us remove parenthesis.
[tex]5g-5g[/tex]
Upon combining terms, we will get:
[tex]5g-5g=0[/tex]
Since [tex]5g+(-5g)[/tex] simplifies to 0, therefore, expression [tex]5g+(-5g)[/tex] is a correct choice.
4. [tex]\frac{1}{2}g+\frac{1}{2}g-\frac{2}{3}g+\frac{2}{3}g[/tex]
Let us combine the terms as:
[tex]\frac{1+1}{2}g-\frac{2}{3}g+\frac{2}{3}g[/tex]
[tex]\frac{2}{2}g-\frac{2}{3}g+\frac{2}{3}g[/tex]
[tex]g-g(-\frac{2}{3}+\frac{2}{3})[/tex]
[tex]g-g(0)[/tex]
[tex]g-(0)=g[/tex]
Since [tex]\frac{1}{2}g+\frac{1}{2}g-\frac{2}{3}g+\frac{2}{3}g[/tex] simplifies to [tex]g[/tex], therefore, expression [tex]\frac{1}{2}g+\frac{1}{2}g-\frac{2}{3}g+\frac{2}{3}g[/tex] is not a correct choice.
