The rules for adding algebraic expressions involve combining like terms. Here's a step-by-step guide:
Steps to Add Algebraic Expressions
According to the reference provided, adding algebraic expressions involves the following steps:
- Step 1: Collect all like terms. Like terms are terms that have the same variable(s) raised to the same power.
- Step 2: Find the sum of the numerical coefficients of all the like terms. The numerical coefficient is the number that multiplies the variable(s).
- Step 3: Write the required sum as the like term whose numerical coefficient is the number obtained in the second step. This means you combine the coefficients and keep the variable part the same.
Example
Let's illustrate with an example:
Add the expressions: 3x + 2y + 5x - y
- Collect Like Terms: Group the 'x' terms together and the 'y' terms together.
(3x + 5x) + (2y - y) - Find the Sum of Coefficients: Add the coefficients of the 'x' terms (3 + 5 = 8) and the coefficients of the 'y' terms (2 - 1 = 1). Note that "-y" is the same as "-1y".
- Write the Result: Combine the new coefficients with their corresponding variables: 8x + 1y, which simplifies to 8x + y.
Therefore, 3x + 2y + 5x - y = 8x + y
