How do you multiply polynomials

Answer 1

Hi Jose!

Multiplying polynomials can be tricky! Let's try one together.

If 7(x - 2) = 3x - 2, then what is the value of x?

Step 1. You will first multiply 7 by x and by -2 on the one side of the equation because you want to get rid of those parentheses. This will allow you to have a fully formed equation that you can then work with. Once you do that, your new equation looks like this: 7x - 14 = 3x - 2.

Step 2. Next, you will want to make sure that both X's are one one side of the equation together, and both the numbers without the X are one one side of the equation together. To do that, first add 14 to both sides. The reason you do this is that allows you to take 14 away from the 7x side making it zero, and then adds it to the other side of the equation. Then, you will subtract the 3x from the other side of the equation because you want to do the same thing you did with the 14 to make it zero on that side. Now that you have done that, your new equation looks like this: 7x - 3x = -2 + 14.

Step 3. Now to do some math. What you will do now is known as simplifying the equation. What this means is taking these numbers and combining them so that you have the simplest equation possible to solve. Let's start with the -2 + 14. When you add a negative number and a positive number together, that's doing subtraction. It sounds complicated, but let's look at it. If you take 14 and subtract 2, you will get 12. If we look at this on a number line, you would look at the number 14 and then take 2 away because you have a negative from it, still getting 12. So now our equation looks like 7x - 3x = 12. But it's still not fully simplified yet. We still need to simplify the X side of the equation. Let's take 7x minus 3x. The X stays because we still don't know what that is, so essentially we're subtracting 7 and 3 which gives us 4. That leaves us with 4x. So now our new equation is 4x = 12.

Step 4. We're almost done! Now we can FINALLY solve for X. I know, it's taken us a while to get there, but hang with me here. To get X on one side of the equation by itself, which is what we have been trying to do all along here, we need to divide by 4. The reason is, is what we're actually seeing in 4x is 4 times X, so in order to remove 4 from that side of the equation, we have to divide by 4. So now if we divide by 4 on both sides of the equation, X is now by itself, and when we divide 12 by 4, we get 3.

So now we know, X = 3. You did it!