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Area of Large Rectangle: Use a 2x3 box method to multiply (x + 5)(x + 9). 2. Area of Small Rectangle: Use a...

1. Area of Large Rectangle:
Use a 2x3 box method to multiply (x + 5)(x + 9).
2. Area of Small Rectangle:
Use a 2x2 box method to multiply (x + 2)(x + 4).
3. Area of Shaded Region:
Subtract the areas (two equations).
4. Write a Word Problem:
Write a real-world word problem to explain what the large rectangle and the smaller rectangle could represent and why you subtract the smaller area from the larger area.

Answer

  1. Area of Large Rectangle: Use the box method to multiply (x + 5)(x + 9):

    x 9
    5

    Calculate each box:

    • x * x = x²
    • x * 9 = 9x
    • 5 * x = 5x
    • 5 * 9 = 45

    Combine: x² + 9x + 5x + 45 = x² + 14x + 45

  2. Area of Small Rectangle: Use the box method to multiply (x + 2)(x + 4):

    x 4
    2

    Calculate each box:

    • x * x = x²
    • x * 4 = 4x
    • 2 * x = 2x
    • 2 * 4 = 8

    Combine: x² + 4x + 2x + 8 = x² + 6x + 8

  3. Area of Shaded Region: Subtract the areas:

    (x² + 14x + 45) - (x² + 6x + 8)

    = x² + 14x + 45 - x² - 6x - 8

    = 8x + 37

  4. Write a Word Problem: A garden is in the shape of a large rectangle, and a smaller rectangular flower bed is placed inside it. The garden measures (x + 5) by (x + 9) meters, while the flower bed measures (x + 2) by (x + 4) meters. Calculate the area of the garden that is not occupied by the flower bed.

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