1. Polynomials and Algebra Tiles

2. Modeling Polynomials Algebra tiles can be used to model expressions.
Algebra tiles can also be used to simplify algebraic expressions such as polynomials.

3. Modeling Polynomials Different shapes represent different values.
Blue square = x2
Red square = -x2

4. Modeling Polynomials Different shapes represent different values.
Green rectangle = x.
Red rectangle = -x.

5. Modeling Polynomials Different shapes represent different values.
Yellow small square = 1
Red small square = -1

6. Modeling Polynomials x2 x 1
- x2
- x
- 1

7. Zero Pairs
The following models are called zero pairs because they are additive inverses of each other.
When put together, they cancel each other out to model zero.

8. Zero Pairs

9. Modeling Polynomials
Represent each of the following with algebra tiles, draw a pictorial diagram of the process, then write the symbolic expression.
2x2 4x 3

10. Modeling Polynomials
2x2 4x 3

11. Distributive Property
3(x+2)
Three is the quantity, so we need three groups of (x+2)

12. Distributive Property
3(x + 2)
3(x) + 3(2)
3x + 6

13. Distributive Property
Represent the quantity 3(x- 4)
3(x – 4)
3(x) – 3(4)
3x – 12

14. Ready to Simplify Addition can be viewed as “combining”.
Combining involves the forming and removing of all zero pairs.
For each of the given examples, use algebra tiles to model the addition.
Draw pictorial diagrams which show the modeling.

15. Simplifying Expressions
x x – 4
Regroup to put like terms together

16. Simplifying Expressions
Make Zero Pairs to Simplify
New expression 3x - 2

17. More Polynomials
Represent each of the given expressions with algebra tiles.
Draw a pictorial diagram of the process.
Write the symbolic expression.
x + 4

18. More Polynomials
2x + 3
4x – 2

19. More Polynomials
Use algebra tiles to simplify each of the given expressions. Combine like terms. Look for zero pairs. Draw a diagram to represent the process.
Write the symbolic expression that represents each step.
2x x + 2
-3x x + 3

20. More Polynomials
What is 2x x + 2?
2x x + 2 = 3x + 6

21. More Polynomials
What is -3x x + 3?
-3x x +3 = -2x + 4

22. Simplifying Polynomials Using Algebra Tiles is easy…
Continue to the lesson and work the practice problems using algebra tiles. For each problem sketch each polynomial and simplify each expression.