In this section, algebraic tiles are used to build and factor trinomials.

Example 1: Use algebraic tiles to create a diagram of (x + 2)(x + 3)

The rectangular tiles represent x:

The square tile represents the constant:

Example 2: Watch as the tiles below are moved to create an algebraic tile diagram of (x − 2)(x + 1)

Interactive exercise. Assistance may be required.
X=rectangle, -x=green rectangle, 1=square, -1 =green square

Example 3: Watch as the tiles below are moved to create an algebraic tile diagram which we will use to find the product of (x − 1)(x − 2).

Interactive exercise. Assistance may be required.

To find the product of (x − 1)(x − 2):

  1. Start with the tile diagram created above:
    Vertical x+1 green square, horizontal x+2 green square
  2. Draw a vertical and horizontal line on the inside of the horizontal and vertical tiles as shown.
    Above picture plus vertical and horizontal lines
  3. Draw horizontal lines extending the ends of the original vertical tiles.
  4. Draw vertical lines extending the ends of the original horizontal tiles. The object is to create a rectangle with the length and width of the factors of the trinomial.
  5. Reading the diagram:
    1. The large red square tile is x2.
      Above picture with red x by x square outlined
    2. The small unit square tile in the upper left corner is shaded in to show a negative; therefore, the entire row is shaded in.
    3. The small unit square tiles in the bottom right are shaded in to show a negative number; therefore, the last two columns are shaded in. But, the top two unit square tiles in the upper right hand corner are already shaded.

      Remember, a negative multiplied by a negative is a positive. Since the shaded areas are negative numbers and the top two unit squares are already shaded, they would change to not shaded because it is the same as a negative multiplied by a negative number or no shading.
    1. The last step is reading the diagram.
    • The large square tile is: x2
    • Three long shaded rectangular tiles: -3x
    • The two small square tiles: 2

    The product of (x − 1)(x − 2) is: x2 − 3x + 2

Example 4: Create a diagram with the tiles and find the product of (x + 2)(2x − 3)

Watch as the tiles below are moved to create the diagram of (x + 2)(2x − 3)

Interactive exercise. Assistance may be required.

Using the diagram just created, watch as the tiles below are moved to form a rectangle to find the product of
(x + 2)(2x − 3):

Interactive exercise. Assistance may be required.

The product of (x + 2)(2x − 3) is __?__
Interactive popup. Assistance may be required.

Check your answer

2x2 + x − 6 (Two large square tiles (+) plus 4 positive rectangular tiles plus 3 negative rectangular tiles plus 6 negative tiles.) Close Pop Up