- Identify like terms by grouping constants (\(-5, 4\)) and the variable terms (\(b, -3b\) and \(2a^2\)).
- Combine the coefficients of like terms: \(-5+4=-1\) and \(1-3=-2\).
- Aggregate the results to obtain the simplified expression \(\boxed{2a^2 - 2b - 1}\).
Explanation
- Identify Like Terms
To simplify the algebraic expression \(-5 + b + 2a^2 - 3b + 4\), we need to group and combine terms that are similar. Like terms are those that contain the same variable raised to the same power, or constant terms. We identify the terms in our expression as follows:
- The constant terms are \(-5\) and \(4\).
- The terms involving the variable \(b\) are \(b\) and \(-3b\).
- The term involving \(a^2\) is \(2a^2\).
- Combine Like Terms
Now, we combine the coefficients of these like terms:
- For the constant terms: \(-5 + 4 = -1\).
- For the terms involving \(b\): \(1b - 3b = (1 - 3)b = -2b\).
- For the term \(2a^2\), there are no other terms with \(a^2\) to combine it with.
- Final Simplified Form
Finally, we arrange the results of our operations into a single expression. Combining the simplified parts, we get:
\[2a^2 - 2b - 1\]
This is the expression in its simplest form. Since none of the provided choices exactly match \(2a^2 - 2b - 1\), the result is \(\boxed{2a^2 - 2b - 1}\).
Examples
Simplifying algebraic expressions is a fundamental skill used in everyday tasks that involve managing budgets or inventory. For example, if you manage a small supply inventory, you might have different types of items with varying quantities (e.g., \(2a^2\) represents a stock of boxes, \(-2b\) represents items removed from shelves, and \(-1\) represents a single missing item). Combining these terms helps you quickly calculate the net count of your inventory in a concise, organized way.