When expanding two binomials using algebra tiles, arrange your binomials so that one is up horizontal, and the other is done vertically. For example, when doing the equation (x+1)(2x-3), you will arrange the binomials like this.
For all tiles, the red side is negative and any other colour is positive. First, multiply the x tiles. You have x(2x) which makes 
, so you use 2 positive 
tiles. Then you look at x and -3. When you multiply these two, you get 3x. So now you know that the final answer will be 
and something. Then, look at 2x(1). By multiplying, we know this is 2x. If we add 2x and -3x together, we can find that the x value will be -1x. Finally, we look at the two constants, 1 and -3. When multiplying, we get -3. So our final answer will be 
, much like this.
When factoring a trinomial, you simply do the opposite of the steps you took when expanding two binomials. For example, when we have the trinomial 
, we lay the tiles out, the to the top left, and arranging the rest of the tiles to make a perfect(ish) rectangular form like this.
Firstly, you must realize the 
is negative, therefore one of the x must be positive, whereas the other one is negative. However, we can also see that -2 on the bottom right corner is negative too. Now we must look at the 5x. 4x is stacked together on the bottom left side, and there is an x in the top right corner. Because of this, we can use common sense to realize that the 2x on the top will be negative. Using this information, we can find the x on the side will be positive. Furthermore, because the lone x on the right side is positive, but we know the x on the left binomial will also be positive, we know the constant on the top binomial will be +1. Now we have one binomial -2x+1, and we know the x on the left binomial is positive. Finally, using the process of elimination, we can find the constant on the left binomial will be negative with a -2.
So, we can find the two binomials will be (-2x+1) and (x-2), much like this.
