Final answer:
By expanding the binomial (x + 3)^2, we found it equals x^2 + 6x + 9, which has an additional term 6x not found in x^2 + 9. Additionally, evaluating both expressions with x = 1 yields different results, confirming they are not equivalent.
Step-by-step explanation:
We will show that the expressions (x + 3)^2 and x^2 + 9 are not equivalent using two different methods.
Method 1: Expand the Binomial
First, we will expand the binomial:
(x + 3)^2 = x^2 + 2(3)x + 3^2 = x^2 + 6x + 9
Comparing this with x^2 + 9, we can see there is an extra term, 6x, which is not present in x^2 + 9. Hence, the two expressions are not equivalent.
Method 2: Evaluate with a Specific Value
Next, let's evaluate both expressions using a specific value for x. Let x = 1:
- (1 + 3)^2 = (4)^2 = 16
- 1^2 + 9 = 1 + 9 = 10
The results are different, so the expressions are not equivalent. This demonstrates that regardless of the value chosen for x, the two expressions will yield different results unless by coincidence.