How do you sum algebraic expressions?

To sum algebraic expressions, you must combine like terms after simplifying the expressions. Here's a step-by-step breakdown of the process, incorporating the reference information provided:

Steps to Sum Algebraic Expressions

Here's a table summarizing the process:

Step	Action	Description
1	Write expressions with an additional symbol	Use '+' to indicate the addition of expressions, this is not required if there is only 2 expressions, but useful for more than 2
2	Open brackets and multiply signs	Remove brackets, paying close attention to the sign preceding the bracket. A minus sign changes the signs of terms within the bracket.
3	Combine like terms	Identify and group terms that have the same variables raised to the same powers.
4	Add coefficients	Perform the addition (or subtraction) of the numerical coefficients of the like terms.

Detailed Explanation with Examples

Here’s a detailed look into each step, with examples to illustrate the process:

1. Write the given algebraic expressions using an additional symbol (Step 1):

   • To add several algebraic expressions, we start by writing the given expressions using the '+' symbol in between them. For example, to sum (2x + 3y) and (4x - 2y), you would write them as (2x + 3y) + (4x - 2y).

2. Open the brackets and multiply the signs (Step 2):

   • Now, remove the brackets, paying close attention to the signs. For example:
     • (2x + 3y) + (4x - 2y) becomes 2x + 3y + 4x - 2y since a '+' before a bracket does not change the sign of the terms inside it.
     • If we were to add (2x + 3y) and -(4x - 2y), it would become 2x + 3y - 4x + 2y because a minus sign before brackets inverses the signs of the terms inside.

3. Combine like terms (Step 3):

   • Identify and group terms that have the same variables raised to the same powers. For example: In the expression 2x + 3y + 4x - 2y , 2x and 4x are like terms, and 3y and -2y are like terms.

4. Add the coefficients (Step 4):

   • Perform the addition or subtraction of the numerical coefficients of the like terms:
     • In our example, 2x + 4x = 6x and 3y - 2y = 1y, or just y.
     • So, the sum of (2x + 3y) and (4x - 2y) is 6x + y.

Additional Tips

• Order: It’s helpful to rearrange terms to have like terms together. For example: 2x + 4x + 3y - 2y.
• Care with Signs: Pay extra attention to negative signs both inside and outside brackets.
• Variables: Remember that variables with no written coefficient have a coefficient of 1 (e.g., y = 1y).

Examples

• Example 1: Add (5a + 2b - c) and (2a - 3b + 4c)

  • (5a + 2b - c) + (2a - 3b + 4c)
  • 5a + 2b - c + 2a - 3b + 4c
  • (5a + 2a) + (2b - 3b) + (-c + 4c)
  • 7a - b + 3c

• Example 2: Add (3x^2 + 4x) and (-2x^2 - x + 5)

  • (3x^2 + 4x) + (-2x^2 - x + 5)
  • 3x^2 + 4x - 2x^2 - x + 5
  • (3x^2 - 2x^2) + (4x - x) + 5
  • x^2 + 3x + 5

By following these steps, you can effectively sum algebraic expressions by combining like terms.