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 = x2

Red square = -x2

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

x2

x

1

- x2

- x

- 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.

2x2

4x

3

Modeling Polynomials

2x2

4x

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)

3x + 6

Distributive Property

Represent the quantity 3(x- 4)

3(x – 4)

3(x) – 3(4)

3x – 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 + 2x – 4

Regroup to put like terms together

Simplifying Expressions

Make Zero Pairs to Simplify

New expression 3x - 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

2x + 3

4x – 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.

2x + 4 + x + 2

-3x + 1 + x + 3

More Polynomials

What is 2x + 4 + x + 2?

2x + 4 + x + 2 = 3x + 6

More Polynomials

What is -3x + 1 + x + 3?

-3x + 1 + x +3 = -2x + 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.