Question

Write an expression to represent the area of the shaded region

Answer 1

Answer:
`3\text{x}^2 - 21`

Step-by-step explanation

Use the FOIL rule to find the area of each rectangle.

• larger = (2x+5)(2x-5) =
  `4\text{x}^2-25`
• smaller = (x+2)(x-2) =
  `\text{x}^2-4`

The difference of squares rule can be used as a shortcut for each.

Then we subtract the rectangle areas to get the shaded region area.

`\text{shaded} = \text{larger} - \text{smaller}\\ \text{shaded} = (4\text{x}^2-25)-(\text{x}^2-4)\\ \text{shaded} = 4\text{x}^2-25-\text{x}^2+4 \ \ \text{ ... see note below}\\\text{shaded} = 3\text{x}^2 - 21`

Note: make sure to distribute the negative sign to each term inside the parenthesis for
`(\text{x}^2-4)`. Many students forget to do this.