The expression to represent the new area of the garden after changes will be N = x² + 20x + 84
A rectangular garden with the dimensions in terms of x is mentioned.
Dimensions length and width have a relation between them.
Taking Width as 'x', It is said that the length of the original garden is 8 feet more than its width. Length = x +8. To calculate the area of the original garden we have the formula for the Area of the rectangle: Length * Width
for the original dimensional garden, the Expression for Area will be :
=> A = L * W => A = (x+8)*x
=> A = x² + 8x
Now when the Dimensions of the garden are extended by 6 feet :
L = (x+8+6) => L = x + 14
W = (x+6)
Expression for the modified Area of the Garden will be :
=> N = (x+14)*(x+6) => x² + (14+6)x + 14*6 {using identity}
=> N = x² + 20x +84
Hence, the expression for the new Area will be N = x² + 20x +84
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