Algebra tiles are manipulatives that represent monomial terms in polynomials, allowing students to physically perform operations like addition, subtraction, multiplication, and factoring. Key tiles are: squares for x^0 terms, rectangles for x^1 terms, and larger squares for x^2 terms, with corresponding red tiles representing negative coefficients. Examples show using the tiles to work through problems like -2x^2 + x - 3 and factoring x^2 - 3x + 2. The document provides a hands-on approach to learning algebra using physical representations of monomial terms.

1. Algebra Tiles By: Bryan Carlo Licudan

2. What are algebra tiles? Algebra tiles are manipulative with which you can represent polynomials and perform polynomial operations. Each tile represents a specific monomial. LgSquare = x2 Rectangle = x Square = 1 LgRed Square = -x2 Red Rectangle = -x Red Square = -1

3. Example An example would be -2x2 + x -3 Square = 1 Lg Red Square = -x2 Lg Red Square = -x2 Rectangle = x

4. Add and subtract Addition & Subtraction Addition and subtraction are performed by combining or removing tiles. Once again, keep in mind that a green tile and a red tile of equal size cancel to leave zero. When subtracting you may need to use this idea in reverse and add zero to a polynomial. (x4 + 6x + 3) + (x1 - x - 2) (8x1 + 2x - 3) - (3x3 + 6x)

5. Example (9x+8x) – (3x+2x) + - + 9X 8 X 3X 2X - 17X 5X X=12

6. Multiplication Multiplying polynomials using algebra tiles is a lot like using the array or area approach to multiplying whole numbers. Illustrated below is the multiplication fact (x-2)(x+1) = x2 - x - 2.

7. Example Multiply (x-2)(x+1) = x2 - x - 2 x + 1 x -2 This figure actually shows that (x-2)(x+1) = x2 - 2x + x - 2 = -1 = -x x2 x = x -2 -2x = 1

8. Factor Factoring To factor try to reverse the multiplying process. For example, to factor x2 - 3x + 2, arrange the appropriate tiles into a rectangular array and determine which factors would give this array. When factoring you may need to add some red and green tiles of equal size. Remember that you need to be able to make a rectangular array. If you can't make such an array, your polynomial can't be factored over the integers

9. The end End of algebra tiles