Hi, Norma. Do the instructions for the problem say something like "expand," "simplify," "multiply," or "write in standard form"? If so, what you need to do is use the FOIL technique. FOIL is an acronym for "first, outside, inside, last".
First, multiply the first term of the left binomial and the first term of the right. You are multiplying 3x times x, which gives you 3x2.
Next, multiply "outside" terms, i.e. the 3x and the 4. The product is 12x.
Then, multiply the inside terms, which are -2 and x. The product is -2x.
Finally, multiply the last two terms (-2 and 4) to get -8.
You now have 3x2+12x-2x-8. Take a look at the answer and look for any like terms.
The 12x and -2x are like terms that combine to give 10x, so your final answer is:
3x2+10x-8
Bob A.
FOIL is Not a technique and is not a method.
FOIL is a mnemonic (not an acronym) to remember some steps to do.
The technique or method you use is distribution,
based on the distributive property of multiplication.
You should learn that you are distributing, Not foiling.
FOIL will Only work for two binomials - it will fail for anything else.
Distribution Always Works.
Also it does not matter what order you do the distribution in.
First Outer Inner Last (FOIL), Outer Inner Last First (OILF), LIOF or any other order will work.
Think of FOIL to help you remember what to do for binomials Only in the beginning.
Then try it using different orders. See how you are distributing the terms.
Look at the distributive property of multiplication and compare it to FOIL, LIOF, etc.
Then forget it and only think of distribution.
Now you will Understand what is happening;
and will be able to work with any king of polynomial, and won't forget it.
08/22/14