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

User Echeg
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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.

User Kmeixner
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