What is an equivalent expression for 3a + 6ab + 9ab - 3(a + ab)?A) 6a - 12ab B) 6a + 14ab C) 6a + 18ab D) 12abCORRECT=BRAINLIST

The given expression is [tex]3a+6ab+9ab-3(a+ab)[/tex]

We see from the possible answers they are all in reduced form - variables are grouped together. That means we should also reduce the given expression to see which answer is equivalent to it.

[tex]3a+6ab+9ab-3(a+ab)[/tex]

Let's expand the term inside the parentheses first, by multiplying each term inside by the coefficient of the parentheses, -3.
[tex]3a+6ab+9ab-3a-3ab[/tex]

Now let's group terms which have the same variables.
[tex]3a-3a+6ab+9ab+3ab[/tex]

We can see that there are two groups:
[tex]3a-3a[/tex]
[tex]6ab+9ab-3ab[/tex]

Let's evaluate them separately. We just need to reduce each group now, since we've already grouped similar terms.
[tex]3a-3a=0[/tex]
[tex]6ab+9ab-3ab=12ab[/tex]

If we put the groups back together into the expression,
[tex]3a-3a+6ab+9ab-3ab=(3a-3a)+(6ab+9ab-3ab)=0+12ab=12ab[/tex]

We can see that [tex]3a+6ab+9ab-3(a+ab)=12ab[/tex]. So (D) is the answer. Hope this helped.