Question

How to solve and draw the model

Answer 1

For expressions x(3x-2), (x+1)(x+2), (3x+1)(x-2), and (x-3)(x-1), area models were used to represent the products as sums:
`\(x^2 - 2x\)`,
`\(x^2 + 3x + 2\)`,
`\(3x^2 - 5x - 2\)`, and
`\(x^2 - 4x + 3\)`, respectively.

a. x(3x-2):

To represent x(3x-2) as a sum, we use an area model. Draw a rectangle with dimensions x and 3x-2. The area of the rectangle is the product.

The area model shows two rectangles: one with dimensions \(x\) and the other with dimensions 3x-2. The total area is the sum of the areas of these two rectangles.

`\[x(3x-2) = x \cdot x + x \cdot (-2) = x^2 - 2x\]`

b. (x+1)(x+2):

Similarly, draw a rectangle with dimensions x+1 and x+2. The area of the rectangle is the product.

The area model shows two rectangles: one with dimensions \(x+1\) and the other with dimensions x+2. The total area is the sum of the areas of these two rectangles.

`\[(x+1)(x+2) = (x+1) \cdot x + (x+1) \cdot 2 = x^2 + 3x + 2\]`

c. (3x+1)(x-2):

Draw a rectangle with dimensions 3x+1 and x-2. The area model shows two rectangles, and the total area is the sum of their areas.

`\[(3x+1)(x-2) = (3x+1) \cdot x + (3x+1) \cdot (-2) = 3x^2 - 5x - 2\]`

d. (x-3)(x-1):

Draw a rectangle with dimensions x-3 and x-1. The area model represents the product as the sum of two rectangles.

`\[(x-3)(x-1) = (x-3) \cdot x + (x-3) \cdot (-1) = x^2 - 4x + 3\]`

The question probable may be:

Write the product of the following expressions as a sum using an area model:

a. x(3x-2)

b. (x+1)(x+2)

c. (3x+1)(x-2)

d. (x-3)(x-1)