Exercise 106 Page 125

Practice makes perfect

a An area model has the shape of a rectangle, which means its area is calculated by multiplying its length and width.

If (x+3)(2x+1) describes the area of the rectangle, one factor will represent the width and the other represents the length.

By separating the sum contained within each factor, we can create four smaller rectangles within the area model.

Let's perform the multiplications.

Since the product of the sides and the sum of the smaller rectangle's area both describe the big rectangle's area, we can equate these expressions. (x+3)(2x+1)=2x^2+x+6x+3 ⇕ (x+3)(2x+1)=2x^2+7x+3

b Like in Part A, we will create an area model by letting 2x and (x+5) represent the length and width of the area model.

By separating the sum contained within the second factor, we can create two smaller rectangles within the bigger one.

Let's perform the multiplications.

Since the product of the big rectangle's sides and the sum of the smaller rectangle's area both describe the big rectangle's area, we can equate these expressions. 2x(x+5)=2x^2+10x

c Like in Part B, we will create an area model by letting x and (2x+y) represent the length and width of the area model.

By separating the sum contained within the second factor, we can create two smaller rectangles within the model.

Let's perform the multiplications.

Since the product of the area model's sides and the sum of the smaller rectangle's area both describe the area, we can equate these expressions. x(2x+y)=2x^2+xy

d Like in previous parts, we will create an area model where the length and width matches the factors of the expression.