Let's define the situation step by step and translate it into a mathematical equation.

1. Let x represent the side length of the original square garden plot.

   • The area of the original square plot is: $A_{\text{square}} = x^2$

2. After the expansion, Shaniah plans to:

   • Double the length of the plot, so the new length is $2x$.
   • Decrease the width by 2 feet, so the new width is $x - 2$.

   Therefore, the area of the expanded rectangular plot is: $A_{\text{rectangle}} = 2x(x - 2)$

3. The new rectangular plot's area is said to be 96 square feet larger than the original square plot, which gives us the following relationship: $A_{\text{rectangle}} = A_{\text{square}} + 96$

4. Substituting the expressions for the areas into this equation: $2x(x - 2) = x^2 + 96$

5. Now, simplify the equation to put it in standard form:

   First, expand the left-hand side: $2x(x - 2) = 2x^2 - 4x$

   The equation becomes: $2x^2 - 4x = x^2 + 96$

6. Move all terms to one side to set the equation equal to zero: $2x^2 - 4x - x^2 - 96 = 0$

   Simplify: $x^2 - 4x - 96 = 0$

Final Equation (Standard Form):

$x^2 - 4x - 96 = 0$

This is the standard form of the equation that represents the problem.

Would you like to go into more detail on solving this equation, or do you have any questions?

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Here are five related questions:

1. How do you solve quadratic equations like this one?
2. What is the significance of "standard form" in algebraic equations?
3. What does it mean when a quadratic equation has no real solutions?
4. How do changes in length and width affect the area of a rectangle?
5. How can you use quadratic equations in real-life situations?

Tip: Quadratic equations often have two solutions, but both might not always be practical for real-world problems. Always verify which solution makes sense for the context.