Polynomials and Algebra Tiles Modeling Polynomials Algebra tiles

Polynomials and Algebra Tiles

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

Modeling Polynomials ¢ Different shapes represent different values. ¢ Blue square = x 2 ¢ Red square = -x 2

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

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

Modeling Polynomials x 2 - x 2 x -x 1 -1

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. ¢

Zero Pairs

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

Modeling Polynomials 2 x 2 4 x 3

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

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

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

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. ¢

Simplifying Expressions x+2 + 2 x – 4 Regroup to put like terms together

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

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

More Polynomials 2 x + 3 4 x – 2

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. 2 x + 4 + x + 2 -3 x + 1 + x + 3 ¢

More Polynomials What is 2 x + 4 + x + 2? 2 x + 4 + x + 2 = 3 x + 6

More Polynomials What is -3 x + 1 + x + 3? -3 x + 1 + x +3 = -2 x + 4

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.