If X is a real number, what is the simplified value of X^2 + X^2?

Introduction / Context:
This is a basic algebraic simplification problem. It tests your understanding of combining like terms, especially terms involving the same power of a variable. Recognizing like terms and adding their coefficients correctly is a foundational skill in algebra.

Given Data / Assumptions:

• Expression: X^2 + X^2.
• X is any real number.
• We follow standard algebraic rules for combining like terms.

Concept / Approach:
Like terms are terms that have the same variable raised to the same power. Here, both terms are X^2. When adding or subtracting like terms, we keep the variable part unchanged and add or subtract the numerical coefficients. So X^2 + X^2 can be seen as 1×X^2 + 1×X^2, which becomes (1 + 1)×X^2.

Step-by-Step Solution:
Recognize that X^2 is a like term with itself, so we treat each as having coefficient 1: X^2 = 1 × X^2.Rewrite the expression: X^2 + X^2 = 1 × X^2 + 1 × X^2.Add the coefficients: 1 + 1 = 2.Thus, X^2 + X^2 = 2 × X^2, commonly written as 2X^2.

Verification / Alternative check:
Substitute a specific value for X, for example X = 3. Then X^2 + X^2 becomes 9 + 9 = 18.Compute 2X^2 with X = 3: 2 × 9 = 18. Both expressions give the same result, confirming the simplification.

Why Other Options Are Wrong:
4X would be the sum of two terms 2X + 2X, not X^2 + X^2, so it confuses first-degree and second-degree terms.2X represents combining X + X, again mixing up the degree of the term.X/2 does not follow from any standard rule for adding like terms and is unrelated to the given expression.

Common Pitfalls:
Some learners mistakenly add the exponents when adding, writing X^2 + X^2 as X^4, but this is incorrect because exponent addition applies to multiplication, not to addition.Another mistake is to confuse X^2 + X^2 with X + X and thus incorrectly conclude that the result should be 2X.

Final Answer:
Using the rule for combining like terms, the simplified value of X^2 + X^2 is 2X^2.