Question

What is an equivalent expression for 3a + 6ab + 9ab - 3(a + ab)?

Answer 1

The given expression is $3a+6ab+9ab-3(a+ab)$

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.

$3a+6ab+9ab-3(a+ab)$

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

Now let's group terms which have the same variables.
$3a-3a+6ab+9ab+3ab$

We can see that there are two groups:
$3a-3a$
$6ab+9ab-3ab$

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

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

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