Question

Determine if the following expressions are equivalent: (x + 4)^2 + (x + 7)^2 and x^2 + 16 + x^2 + 49.

Answer 1

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.