Once you see the common $(a - 2)$, rewrite the expression as $(a - 2)(\text{something})$. What is left from each term after you take out $(a - 2)$?

After factoring out $(a - 2)$, add together the remaining parts from each term to form the expression inside the parentheses.

In Desmos, type the original expression using $x$ instead of $a$: y = 7x(x - 2) + 3(x - 2).

On new lines, type each option (again using $x$):

• y = (x - 2)(7x - 3)
• y = (x + 2)(7x + 3)
• y = (x - 2)(7x + 3)
• y = 10x(x - 2)

Look at the graphs: the correct choice will have a graph that lies exactly on top of the graph of the original expression for all $x$. You can also use a table (click the gear icon next to an equation and enable the table) to check that the $y$-values match the original expression for several $x$-values.

Look at both terms in the expression $7a(a - 2) + 3(a - 2)$.

• The first term is $7a(a - 2)$.
• The second term is $3(a - 2)$.

Both terms contain the factor $(a - 2)$, so you can factor $(a - 2)$ out of the entire expression. That means you want to rewrite the expression in the form

When you factor $(a - 2)$ out of each term, you remove one $(a - 2)$ from each:

• From $7a(a - 2)$ you are left with $7a$.
• From $3(a - 2)$ you are left with $3$.

So the expression becomes

which matches choice C, $(a - 2)(7a + 3)$.