Final answer:
The equivalent form of \((x^2 +1)+(2x -1)\) is \(x^2 + 2x\), which is found by combining like terms.
Step-by-step explanation:
The expression \((x^2 +1)+(2x -1)\) consists of two parts that can be combined together by performing algebraic addition. When we combine like terms, we group the x-squared terms and the constant terms separately, and the x terms after that. So, we add the constant terms (1 and -1) and the x terms (2x) to the x-squared term \(x^2\).
Step by step, it looks like this:
- Combine the x-squared terms: \(x^2 + (nothing) = x^2\).
- Combine the x terms: \((nothing) + 2x = 2x\).
- Combine the constant terms: \(1 + (-1) = 0\).
After combining the like terms, we get:
\(x^2 + 2x + 0\)
Since adding zero does not change the value, we can simplify it further to:
\(x^2 + 2x\)
This is the simplified equivalent form of the original expression.