%2B(x%5E2-2x%2B1).jpeg "(2x^2+1)+(x^2-2x+1)")
Simplifying Expressions: (2x^2 + 1) + (x^2 - 2x + 1)
In algebra, simplifying expressions is a fundamental skill that involves combining like terms to arrive at a more concise representation. Let's explore how to simplify the expression: (2x^2 + 1) + (x^2 - 2x + 1).
Understanding the Expression
This expression consists of two sets of parentheses, each containing a polynomial. The first set, (2x^2 + 1), has two terms: a quadratic term (2x^2) and a constant term (1). The second set, (x^2 - 2x + 1), has three terms: a quadratic term (x^2), a linear term (-2x), and a constant term (1).
Simplifying the Expression
To simplify the expression, we need to remove the parentheses and combine like terms. Since the operation between the parentheses is addition, we can simply drop the parentheses:
(2x^2 + 1) + (x^2 - 2x + 1) = 2x^2 + 1 + x^2 - 2x + 1
Now, we can identify and group like terms:
- Quadratic terms: 2x^2 + x^2 = 3x^2
- Linear term: -2x
- Constant terms: 1 + 1 = 2
Combining these, we get the simplified expression:
3x^2 - 2x + 2
Conclusion
By removing the parentheses and combining like terms, we successfully simplified the expression (2x^2 + 1) + (x^2 - 2x + 1) to 3x^2 - 2x + 2. This process highlights the importance of understanding the rules of algebra and applying them to manipulate expressions effectively.