Question

Consider the following "generic rectangle" where the area of each region is given. Write equivalent

expressions that express the area of the whole rectangle as a sum and as a product.

Answer 1

• sum: 3x² -4x -4
• product: (x -2)(3x +2)

Explanation:

The areas of four regions are given. We can simply add them to find the sum. To express them as a product, we need to look at common factors.

Sum

The total of the given area expressions is ...

3x² +2x -6x -4 = 3x² -4x -4 . . . . sum

Product

Extending the table to show common factors of each row and column, we have ...

`\begin{array}c&3x&2\\\cline{1-3}x&3x^2&2x\\\cline{1-3}-2&-6x&-4\\\cline{1-3}\end{array}`

Since each cell of the table is the product of the corresponding common factors, we can write the area as the product ...

(x -2)(3x +2) . . . . product