Exercise 119 Page 132

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 (2x+1)(2x+1) is the area of the model, one factor will represent its 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. (2x+1)(2x+1)=4x^2+2x+2x+1 ⇕ (2x+1)(2x+1)=4x^2+4x+1

b Like in Part A, we will create an area model by letting 2x and 4x represent the dimensions of the model.

Let's perform the multiplication.

We get the following equation. (2x)(4x)=8x^2

c Like in previous parts, we will create an area model by letting 2 and (3x+5) represent the width and length of the model.

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

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. 2(3x+5)=6x+10

d Like in previous parts, we will create an area model by letting y and (2x+y+3) represent the length and width of the rectangle.

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

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. y(2x+y+3)=2xy+y^2+3y