Answer:
1. Let’s assume that the original garden was a rectangle with width w and length l. After extending it by equal length on two sides, we get a new rectangle with width w+2x and length l+2x. The area of the new rectangle is (w+2x)(l+2x). To find the area of the extended area only, we need to subtract the area of the original garden from the area of the new rectangle. The area of the original garden is wl. Therefore, the polynomial that represents how much square foot of soil you need to cover the extended area only is:
(w+2x)(l+2x) - wl
which can be simplified as:
wl + 2lx + 2wx + 4x^2 - wl
The polynomial can be further simplified as:
4x^2 + 2lx + 2wx
2. If the original garden was extended by 6 ft on each side, then the new garden will be extended by 175% 1.
To calculate this percentage, we can use the formula:
% increase = (new value - old value) / old value * 100%
The original garden has an area of 64 square feet (8 feet x 8 feet). If we extend each side by 6 feet, then the new garden will have an area of 196 square feet (14 feet x 14 feet).
So, using the formula above:
% increase = (196 - 64) / 64 * 100%
% increase = 132 / 64 * 100%
% increase = 206.25%
Therefore, if the original garden was extended by 6 ft on each side, then the new garden will be extended by 206.25% 1.
I hope this helps! Let me know if you have any other questions.
Explanation: