User blog:Forestpaw13/Multiplying two binomials.

'WARNING. VERY CONFUSING.'

Okay, guys, I am going to teach you how to multiply two binomials, using FOIL.

Let's say that our problem is: (x + 3)(x + 6)  You probably think: "Whaat?" and go away.

But FOIL makes it easy.  F- First O- Outside I- Inside L- Last

It looks confusing, but I shall take it step by step.

Okay, the first two terms in this binomial are "x" and "x".  You instantly think, "The answer is 2x!" because there are two "x"s, and you are putting them together.  WRONG.  Instead, you must put these two "x"s together in a different way, the exponential way.  "x" times "x" equals "x2"  An explanation is required, I see.  You see, when you have 22, you multiply 2 times 2.  x2 is essentially the same thing- you multiply "x" times "x". 

So the first term in the final answer is "x2".

Let's take a look at the "O" in FOIL, shall we?  The outside terms in the problem are 6 and "x".  Your answer, quite simply, is 6x. You multiply them together, and since there are not two "x"s, there is no exponent. <BR> Simple enough, right?

The "I" is the same thing- 3 and "x". <BR> Your answer is 3x.

On the L, you multiply the last two terms, which are 3 and 6. <BR> 18.

So... you have four answers. What to do with them?

(x2 + 6x + 3x + 18)

You combine like terms. 6x and 3x are alike you see, because both of them have "x" at the end with no exponent. 18 is not alike because it does not have an "x".

Your final answer:

(x2 + 9x + 18)

See? Not so hard.

Here's some practice problems:


 * 1) (x + 7)(x + 2)
 * 2) (x + 3)(x + 1)
 * 3) (x2 + 2)(x + 3)
 * 4) (2x + 5)(3x + 4)

Good luck! If you have any questions just comment. Forestpaw13 My Talk