Question

A rectangular garden has length and width as given by the expressions below.

Length: 4 - 7(3x + 4y)
Width: 3x(-2y)
Write a simplified expression for the perimeter of the rectangle.

Answer 1

6xy + 21x + 28y - 4

Explanation:

Step 1: Evaluate the length.

4 - 7(3x + 4y)

4 - 21x - 28y

Step 2: Evaluate the width.

3x(-2y)

- 6xy

Step 3: Length + Length and Width + Width

(4 - 21x - 28y) + (4 - 21x - 28y) and (- 6xy) + (- 6xy)

Step 4: Group like terms.

(4 + 4) + (- 21x - 21x) + (- 28y - 28y) and (- 6xy) + (- 6xy)

8 - 42x - 56y and - 12xy

Step 5: Add them all together.

8 - 42x - 56y - 12xy

Step 6: Order the terms.

- 12xy - 42x - 56y + 8

Step 7: Simplify it.

`( - 12xy - 42x - 56y + 8)/( - 2) = 6xy + 21x + 28y - 4`

Final Answer: 6xy + 21x + 28y - 4