Transcript

INSTRUCTOR:

An algebraic expression is just a calculation, but one or more of the letters has been replaced with a symbol. Here we've got an equation that comes from the perimeters problem. P, the perimeter, is found by calculating the sum of the five side lengths-- 3, b, the short side length, a minus 3, b, and a. So our equation says that the perimeter is equal to that sum.

The equation is made out of two expressions. One of them is just a single P for perimeter. And that is equal in value to another expression, which is 3 plus b plus a minus 3 plus b plus a.

If an expression involves addition or subtraction, then the parts that are added or subtracted are called terms. So this expression has five terms. We have 3. We have b. Here we have a more complex term, a minus 3. Then we have b, and we have a.

a minus 3 is written in brackets because we calculated the length of that short side by subtracting 3 from a. But it could be separated into a plus a and a minus 3, which would give us six terms in total. So this is to remind you that an equation is made by saying that two expressions are equal, and the expressions can further be broken down into terms.

Here we look at collecting like terms in an expression. The first step looks at what we've already done. Adding a minus 3 is the same as adding a and then subtracting 3. So our expression now has six terms.

Then we collect together the terms that can be added up or subtracted, the like terms, 3 and here subtract 3. These are both just numbers. So I collect those first. There's an invisible plus at the beginning of the first term. So I have plus 3 then minus 3 that can go together.

Then you'll notice we've got a plus b, another plus b, a plus a, and another plus a. What I've done there is to collect those terms together, bringing the operator sign, the plus or minus, with each term. Now I'm going to make that a shorter expression by collecting the like terms.

Plus 3 minus 3 gives me 0. Plus b plus another b, whatever number b is-- and, of course, b could be any number-- a shorter way of writing that is to say that I'm adding 2 times b. And, similarly, plus a plus another a-- a shorter way of adding two lots of a is to write 2 times a. So we have 0 plus 2 times b plus 2 times a.

Finally, we'll use the convention that, instead of writing 2 times b, we write 2b. And, instead of 2 times a, we write 2a. The final expression is 2b plus 2a. If you look at all the different expressions you found for the perimeter, they will all simplify to 2b plus 2a in their shortest form.