Using Area
It is very simple to identify if expressions are equivalent, by looking at how they represent the area of a figure.
Review the area for a rectangle and circle first.
Look at the two expressions below:
8x² + (πx²/2)
8x² represents the area of the rectangle while (πx²/2) represents the area of the circle. The area of the circle is divided by 2 since it is half of a circle.
6x² + 2x²
+ (πx²/2)
The area of the first rectangle is 6x² and the area of the second rectangle is 2x². These expressions can be added together to get 8x² which is the same area of the rectangle in the first example. The area of the circle is also the same as the first example, (πx²/2).
Even though both expressions are look different, they are equivalent since they both represent the same area of the shape. This is one way to verify an equivalent expression.
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