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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

\((x + 1)(x + 2)\)      

\((2x)(x + 2)\)      

\((2x + 1)(x + 2)\)      

\((x + 1)(x - 2)\)      

\((x - 1)(x - 2)\)      

\((2x + 1)(x - 2)\)      


For each expression in the table above:


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


Multiply the factors together to get a sum of terms.


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


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


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


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?


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


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


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


Use algebra tiles to factor these expressions.


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


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


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