Adding algebraic expressions involves combining like terms to simplify the expression. Here's a step-by-step process, utilizing information from the provided references:
Steps to Add Algebraic Expressions
| Step | Description | Example |
|---|---|---|
| 1 | Write expressions horizontally: Place each expression in brackets and separate them with plus signs. | If we have (2x + 3y) and (4x - y), it becomes: (2x + 3y) + (4x - y) |
| 2 | Group Like Terms: Rearrange the terms so that like terms (terms with the same variable raised to the same power) are next to each other. | (2x + 4x) + (3y - y) |
| 3 | Add Coefficients: Combine the numerical coefficients of the like terms, keeping the variable part. | (2 + 4)x + (3 - 1)y = 6x + 2y |
Detailed Explanation
- Like Terms: Like terms are terms that have the same variable raised to the same power. For example, 3x and 5x are like terms, but 3x and 3x² are not. Similarly, 2xy and 7xy are like terms, but 2xy and 2x are not.
- Coefficients: Coefficients are the numerical parts of a term. For instance, in the term 5x, 5 is the coefficient.
- Combining Like Terms: The key is to only add or subtract the coefficients of like terms. The variable part remains unchanged.
Examples
-
Add (5a + 2b) and (3a - 4b):
- (5a + 2b) + (3a - 4b)
- (5a + 3a) + (2b - 4b)
- 8a - 2b
-
Add (7x² + 3x + 1) and (2x² - x + 5):
- (7x² + 3x + 1) + (2x² - x + 5)
- (7x² + 2x²) + (3x - x) + (1 + 5)
- 9x² + 2x + 6
-
Add (4ab + 6c) , (2ab - 3c + d) and (5ab + 2d)
- (4ab + 6c) + (2ab - 3c + d) + (5ab + 2d)
- (4ab + 2ab + 5ab) + (6c - 3c) + (d + 2d)
- 11ab + 3c + 3d
Practical Tips
- Organization: Keep your work organized by grouping like terms clearly before adding.
- Signs: Pay close attention to the signs (+ or -) in front of each term.
- Constant Terms: Remember to combine constant terms (numbers without variables).
- Missing Terms: If an expression is missing a term, you can add it with a coefficient of zero to help organize your work (e.g., if an expression only has an x² term and a constant, you can treat it as having a 0x term).
By following these steps, you can accurately and efficiently add algebraic expressions.
