MODEL POLYNOMIAL MULTIPLICATION

Algebra tiles can be used to multiply polynomials. Use the length and width of a rectangle to represent the factors. The area of the rectangle represents the product. 

Remember :

(i) The product of two values with the same sign is positive. 

(i) The product of two values with different signs is negative. 

Activity 1

Use algebra tiles to find 2(x + 1). 

Model : 

Place the first factor in a column along the left side of the grid. This will be the width of the rectangle. 

Place the second factor across the top of the grid. This will be the length of the rectangle. 

Algebra :

2(x + 1)

Model : 

Fill in the grid with tiles that have the same width as the tiles in the left column and the same length as the tiles in the top row. 

Model : 

The area of the rectangle inside the grid represents the product. 

Algebra :

=  x + x + 1 + 1

=  2x + 2

Activity 2

Use algebra tiles to find (2x)(2x - 3). 

Model : 

Place tiles to form the length and width of a rectangle and fill in the rectangle.

The product of two values with the same sign (same color) is positive (yellow).  

The product of values with different signs (different colors) is negative (red). 

Algebra :

(2x)(x - 3)

Model :

The area of the rectangle inside the grid represents the product. 

The rectangle has an area of (2x² - 6x), so

(2x)(x - 3)  =  2x² - 6x

Algebra :

=  x² + x² - x - x - x - x - x - x

=  2x² - 6x

Activity 3

Use algebra tiles to find (x + 1)(x - 2). 

Model : 

Place tiles for each factor to form the length and width of a rectangle.  

Fill in the grid and remove any zero pairs. 

Algebra :

(x + 1)(x - 2)

x² - x - x + x - 1 - 1

Model :

The area inside the grid represents the product. 

The remaining area is (x² - x - 2), so

(x + 1)(x - 2)  =  x² - x - 2

Algebra :

x² - x - 1 - 1

x² - x - 2

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