Question #06bd6

When you factor by grouping, you break the expression down into two parts.

#ac+ad+bc+bd# becomes #(ac+ad)+(bc+bd)#

We didn't change anything, we just grouped the left two terms together and the right two terms together.

Now we can factor out a common variable in the broken down expression.

#color(orange)(a)(c+d) + color(orange)(b)(c+d)#

Notice how after we factored out a common variable respective to each grouped portion, we had the same expression left inside the parentheses.

Once you recognize this, you can confirm that the expression can be factored by graphing.

The next step is to group the factored out variables by themselves.

#color(orange)((a+b))(c+d)#

And that is the factored form. Let's review the steps :

1.) Break the expression up into two distinct portions enclosed in parentheses (break up the first two terms into one portion and the last two terms into another)

2.) Look for a common factor/multiple to take out from each portion (they don't have to be the same thing).

3.) Once you factor both portions of the expression, check to make sure the remaining values inside the parentheses match. If they do, the expression can be factored by grouping. If not, they can't.

4.) Assuming that the parentheses match, take the factored value from the first portion and multiply it to the factored value of the second portion.

5.) Now you should have two distinct values each within parentheses.

If these steps don't make sense, look at the way I factored the example above again.