In algebra, you can add or subtract terms if the letters and exponents on the letters are exactly the same. 

So if you have 3bc + 5bc, you can add them because both terms have bc. All you’ll do is add the numbers and bring the common letters after it. Here we’ll add the 3 and the 5 to get 8.

Then bring the bc after it.

The letters can be interchanged and you can still add them. We usually prefer letters arranged in alphabetical order.

so you can add 3bc + 5cb.

I can just rewrite it as 3bc + 5bc.

You cannot add 3 ab + 5ac. Although they both have “A”, you cannot add them because one is ab and the other is ac. Your answer will be 3 ab + 5ac.

You cannot even add 3a + 5 ab. one is just A and the other is AB. Your answer will be 3a + 5 ab.

If the letters have exponents, then the exponents on each letter must be exactly the same.

So you can subtract 5x squared minus 2x squared, to get 3x squared.

You cannot subtract 5x squared minus 2x cubed. The exponents must also be the same to add or subtract.

With this in mind, let’s look at our questions.

 

Question 1.

2ab + 3a minus 6ab =

Here, we see that we have 2ab and minus 6ab. Since they both have ab after the numbers, we can subtract. We subtract 2 minus 6 to get negative 4. Then we bring the common letters ab after it.

Now we cannot work on 3a minus 4ab. One is just A and the other is ab,

so our final answer is 3a minus 4ab.

 

Question 2.

5x² – 2xy + 3x² + 7x³ =

Here, we can work on the 5x squared and the 3x squared. We add the numbers, 5 + 3 to get 8.

Then we bring the x squared after it.

There is nothing else that is like terms. so our final answer is 8x squared minus 2xy plus 7x cubed.

 

Question 3.

ab + 3ac + 2ab – 2ac.

The first thing you’ll notice is that here, we have ab, without any number in front. In algebra if you see just letter, the invisible 1 is implied.

so ab is the same as 1ab.

we can add the ab like terms.

so we add 1 + 2, to get 3ab.

Then we can subtract 3ac minus 2ac.

This will give us 1 ac.

We don’t have to write the 1.

our final answer is therefore. 3ab + ac.