Answer:
The two expressions are equivalent, based on a direct numerical comparison (a) and (b) a methematical comparison.
Explanation:
a) The expressions can be shown to be equivalent by entering the numbers into each expression and comparing the results. This is easy with a spreadsheet program. Set up a table with the values of x in the left column. Then enter the 2 equations in the first entry (-2) in each of two subsequent columns. These expressions can be copied to the other rows by clicking on the first cell and dragging the lower right corner down until all rows are included. The copied expressions will select the corresponding value of x for both expressions, as shown in the attached table. It can be seen that both expressions yield the same results.
b) Prove the equivalence mathematically:
In other words, do the two expressions equal each other?
(12x^2 - 27)/3 = -(-2x+3)(2x+3) ??
Simplify both sides
(4x^2 - 9) = -(-4x^2 + 9) ?
4x^2 - 9 = 4x^2 - 9 Yes. They are equivalent