Working with algebraic expressions: Examples

If you have figured out how to gather like terms in an algebraic expression, then you know how to add and subtract in algebra. Now we're going to do some multiplication as well. Let's start simply. X times five. We write that as five X.

If there's no sign in between, remember: that means multiplication. Okay, what about this one? Three X times four. Well it means just the same as three times X times four. And when we're doing multiplication, the order of the factors doesn't matter.

So you might as well write it like this. Three times four is twelve. And remember, no need to write the multiplication sign between the coefficient and the variable, so it's just... Twelve X! Look at the first and the last row.

Normally you will do all of this at once. Three X times four, equals twelve X. What about this multiplication then? Now we have an X in both factors. Let's write in all the multiplication signs, just to make it clear.

Then we can place all the X:s together at the end, and start from the left. Well, three times two equals six. But what's X times X? It's X squared! Three X, times two X, equals six X squared.

If you think of X here as a distance, say... a metre. Then 3 X times 2 X is a rectangle, with an area of six metres squared. Metre times metre equal metres squared. Just like X times X equal X squared.

Again, you're not going to write all of this into each calculation. When you understand what's happening, you just go from the first to the last row here, in one go. Here, you need to watch out. Note that there's a plus sign in the middle of this expression. So here we must follow the order of operations, which tells us that multiplication comes before addition.

So we do the two multiplications first. Four times five X is 20 X. And three times two X is six X. Now we have two terms of the same kind, so we add those together. And that equals 26 X.

Okay, that's multiplying with one variable. Let's bring in another one. Here, we are asked to multiply X by Y. It's really simple. X times Y is XY.

Remember, if there is no sign written in between, it means multiplication. What about this then? Two X times 3 Y. Well, two times 3 is six, and X times Y is XY. And we miss out the multiplication signs.

Two X times three Y equals six XY. One last example! Here, we combine what we have learned so far. First, multiply the coefficients -- five times two equals ten. Then, multiply the variables: Y times X is YX. (But we write it as XY, to keep the expression in alphabetical order.) And XY times Y...

Is X-Y-squared! Note that it's only the Y that is being squared here. And drop the multiplication sign. Practice this on your own until each of these examples are crystal clear. That should give you a good start with multiplication in algebra!