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)
\(x^2 - 4\)