We can use our set of Algebra Tiles to illustrate adding polynomials.

Click HERE if you need to print and cut out a set of your own Algebra Tiles.

Let us show you each tile and what it stands for:

This tile is the positive one tile.

This is your negative one tile.

If you place the two tiles beside each other, you create a ZERO.
1+(-1)=0

This tile stands for a single x. It is one unit wide and an unknown or "x" number of units long. *NOTE: an even number of "one unit" () tiles will NOT fit on this tile. It is supposed to be a "mystery" size.

This represents the opposite of x, or negative one x.

Placing these two together also creates a ZERO. x + (-x) = 0

Here we have the positive one x squared tile. It measures "x" on both its length and width (both are "mystery" lengths i.e. not multiples of the one unit square). Therefore its area is x^2.

And here we have the opposite of the x square tile, or negative one x squared.

As above, when placed together these tiles create a big, fat, ZERO. x^2 + -x^2 = 0.

Now let's start making some polynomials with our tiles, and we will add them as we go.

To create the binomial 3x^2 + (-2x).....more commonly written as 3x^2-2x, lay these tiles out on our desk.

Now let's add to this the trinomial -5x^2 + 3x +(-2).

Now make all the ZERO'S that you can and pull them off your desk. The tiles that remain will be the answer to the addition problem.

the answer is -2x^2 + x + (-2)

Practice a few with your own tiles. Click the answer links to see if you are correct.

• (-2x^2 + 7) + (8x^2 - 9) = ? answer
  
  
• 3x + x^2 + (-7) plus
  -6x + 7x^2 + 9 = ? answer
  
  
• (-9 + 3x - x^2) + (-4x^2 - 3x - 4) = ? answer
  

Have fun TOUCHING your Algebra!