(-x - 2) * (4y - 3) = 3x -8y -4xy +6
But HOW do you get it?
Actually, the easiest way is to use one of the many factoring calculators you find on the internet. Just Google on "factoring calculator," and you'll find a raft of them, mostly free. Try a few. Pick one you like.
But, if you MUST be traditional, here are some clues for solving this by "inspection." That is a great term. It means keep guessing until you get it.
Here, you see the plus six on the end. The only way to get a plus there is to have the signs alike in the two binomials. They must either be both pluses, or both minuses.
Then you see there are a couple minus terms in what you are trying to factor, That means there is at least one minus sign somewhere. And you know already the signs are alike. So,that proves that the signs in BOTH your binomials will be negative, because you couldn't get a negative in the product AND a positive final number any other way.
So far, you have in your mental picture something like this:
(aaa - bbb) * (ccc - ddd)
Now, bbb times ddd must equal 6. Don't waste time with 1 and 6, because the 3 in front of the x tells you 6 would be impossible; it must be 3, and aaa must be -x in order to make the positive 3x in the expression you're factoring. So, keeping up with your absolutely brilliant logic:
(-x - 2) * (ccc - 3)
It's downhill from here. ccc must be some number of y's that make -8y when multiplied by -2. Duhhhh... Let's try 4y. Bingo! It works.
Checking it out:
(-x - 2) * (4y - 3) = 3x -8y -4xy +6
Okay, go make popcorn.
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