Final answer:
Upon expanding and simplifying both expressions, (a-3)^2 simplifies to a^2 - 6a + 9 while the other complex expression simplifies to a^2 + 72 which are clearly not equal. therefore, the statement is False.
Step-by-step explanation:
To evaluate whether the statement (a-3)² is the same as a² + 9 ² - 9a² - 6a + 9a² + 6a - 9 is true or false, we must first expand the binomial (a-3)² correctly.
Using the formula (x-y)² = x² - 2xy + y², we get:
which simplifies to a² - 6a + 9.
Looking at the expression a² + 9 ² - 9a² - 6a + 9a² + 6a - 9, we can simplify it by combining like terms:
- a² - 9a² + 9a²
- 9 ²
- - 6a + 6a
- - 9
The result of this simplification is a² + 81 - 9, which can be further simplified to a² + 72. This is not equal to a² - 6a + 9. Therefore, the statement is False.