Final answer:
The expressions (x + 4)^2 + (x + 7)^2 and x^2 + 16 + x^2 + 49 are not equivalent.
Step-by-step explanation:
In this question, we need to determine if the expressions (x + 4)^2 + (x + 7)^2 and x^2 + 16 + x^2 + 49 are equivalent.
We can start by expanding both expressions:
(x + 4)^2 + (x + 7)^2 = x^2 + 8x + 16 + x^2 + 14x + 49
x^2 + 16 + x^2 + 49 = 2x^2 + 65
By comparing the expanded expressions, we can see that they are NOT equivalent.
The first expression contains additional terms (8x and 14x) that are not present in the second expression.