What is 2x squared plus x squared
The Correct Answer and Explanation is:
To solve the expression (2x^2 + x^2), we need to combine like terms. In algebra, like terms are terms that contain the same variable raised to the same power. Here, both (2x^2) and (x^2) are like terms because they both involve the variable (x) raised to the second power.
Step-by-Step Solution:
- Identify Like Terms:
- The term (2x^2) represents two instances of (x^2), and the term (x^2) represents one instance of (x^2).
- Combine Like Terms:
- When adding like terms, we simply add their coefficients (the numerical factors in front of the variable). The coefficient of (2x^2) is (2), and the coefficient of (x^2) is (1).
- Therefore, the operation is:
[
2 + 1 = 3
]
- Write the Result:
- After adding the coefficients, we maintain the variable part, (x^2). Thus, we have:
[
2x^2 + x^2 = 3x^2
]
Final Answer:
The simplified expression is (3x^2).
Explanation:
Understanding how to combine like terms is crucial in algebra. It simplifies expressions and makes them easier to work with in equations or further calculations. The principle of combining like terms applies to any algebraic expression, not just those involving variables raised to a power.
When you encounter polynomial expressions, look for terms that share the same variable and exponent. For example, (x^2), (3x^2), and (-5x^2) are all like terms, while (x), (x^2), and (x^3) are not because they differ in their exponents.
By practicing this concept, you’ll gain confidence in manipulating polynomials, which is a foundational skill in algebra and higher-level mathematics. Recognizing patterns and applying basic operations will help you tackle more complex algebraic problems efficiently.