### Student Page 4.3.4 Multiplying and Factoring with Algebra Tiles

Materials: One set of algebra tiles and one algebra tile frame for each pair of students

\((x + 1)(x + 2)\) |
\((2x)(x + 2)\) |

\((2x + 1)(x + 2)\) |
\((x + 1)(x - 2)\) |

\((x - 1)(x - 2)\) |
\((2x + 1)(x - 2)\) |

#### 1.

For each expression in the table above:

##### (a)

In the space provided, draw a picture of an area model to show the product of the two terms.

##### (b)

Multiply the factors together to get a sum of terms.

##### (c)

Replace \(x\) with 7 in both original and final expressions. Check to see that you get the same result in both cases.

#### 2.

Use algebra tiles to work backwards from a product to find two factors that generate that product.

##### (a)

Collect the pieces for \(x^2 + 7x + 12\text{.}\)

##### (b)

Arrange the pieces to form a rectangle. The dimensions of the rectangle are the factors of \(x^2 + 7x + 12\text{.}\) What are the factors?

##### (c)

Repeat Task 4.3.4.2.b using the pieces for \(x^2 + 8x + 12\) and then for \(x^2 + 13x + 12\text{.}\)

##### (d)

Compare your work for all three expressions. What do you notice?

##### (e)

How do the algebra tile pieces help you think about factoring?

#### 3.

Use algebra tiles to factor these expressions.

##### (a)

\(2x^2 + 5x + 3\)

##### (b)

\(2x^2 + 7x + 3\)

##### (c)

How does your work change from one to the next? Discuss the arrangements of tiles. Which tiles should you position first?

#### 4.

Use what you learned in Student Page Exercise 4.3.4.2 and Student Page Exercise 4.3.4.3 to factor the following expressions:

##### (a)

\(x^2 + 4x + 4\)

##### (b)

\(x^2 - 2x - 3\)

##### (c)

\(x^2 - 4\)