Can you show how to collect like terms?

Answer 1

Try this for an explanation:

The problem is to collect like terms in the expression:

1h + 2d - 3sg +4c + 9sb -11gr + 8c + 7d - 4sb + 3gr + 5sg + 9h

Right now, this looks terrible. It's long, it's complicated, and we're not sure what "collect like terms" means anyway.

OK. Forget about that one for just now. We'll come back to it when we can handle it.

First, look at a different list, and see if you can clean it up and make it any simpler.

This is a survey taken at the zoo one afternoon. Here it is:

1 hen, 2 ducks, -3 squawking geese, 4 cows, 9 school buses, -11 gold rings

8 cows, 7 ducks, -4 school buses, 3 gold rings, 5 squawking geese, 9 hens

If you look over this list, you see some duplications. For example, there's 1 hen at the beginning

and 9 more hens at the end. These could be added to get 10 hens.

Also, there are 2 ducks near the beginning, and 7 more ducks in the middle.

They could go together to make 9 ducks.

Next, there are negative 3 squawking geese near the beginning, and positive 5 of them

near the end. Those all go together to make a total of 2 squawking geese.

As complicated as the zoo survey looked at first, here's what you have after you

go through it and combine all the similar items:

10 hens, 9 ducks, 2 squawking geese, 12 cows, 5 school buses, -8 gold rings

This is a lot simpler and cleaner.

Only one more thing to point out: "2 ducks" and "7 ducks" are called "like terms".

They are terms that are alike, because they're both ducks. You collect them, then

you add them to make a single term . . . 2 ducks + 7 ducks = 9 ducks.

Now you're ready to go back to the top, and "collect like terms" in that long bold-faced

expression on the third line.

I have to go on and answer some more questions.

Good luck. You won't have much trouble.