Addition Of Algebraic Expressions
The addition of algebraic expressions is the process of adding together two or more algebraic expressions. Here are the steps to add algebraic expressions:
Step1. Identify like terms: Look at the expressions that you want to add and identify the terms that have the same variables and exponents. For example, if you want to add 2x + 3y + 4x – y, the terms 2x and 4x are like terms, and the terms 3y and -y are like terms.
Step 2. Add the coefficients of the like terms: Once you have identified the like terms, you can add their coefficients. For example, 2x + 4x is 6x, and 3y – y is 2y.
Step 3. Combine the like terms: Finally, combine the like terms with their new coefficients to get the simplified expression. For example, the expression 2x + 3y + 4x – y becomes 6x + 2y.
Example: Simplify the expression 3x2 + 2x – 4x2 – 3x + 5.
Step 1: The terms 3x2 and -4x2 are like terms, and the terms 2x and -3x are like terms, but the constant term 5 is not like any of them.
Step 2: 3x2 – 4x2 is -1x2, and 2x – 3x is -1x.
Step 3: Combine the like terms with their new coefficients and include the constant term: -1x2 – 1x + 5.
The answer is -x2 – x + 5.
Subtraction Of Algebraic Expressions
The subtraction of algebraic expressions is similar to the addition of algebraic expressions, but instead of adding the terms of the expressions that have the same variables and exponents, we subtract them. Here are the steps to subtract algebraic expressions:
Step1.Distribute the subtraction: Rewrite the expression as an addition of the first expression and the opposite of the second expression. For example, to subtract 2x + 3y from 4x – y, we can rewrite it as 4x – y + (-2x – 3y).
Step2. Identify like terms: Look at the expressions you want to subtract and identify the terms that have the same variables and exponents.
Step3. Add or subtract the coefficients: Once you have identified the like terms, you can add or subtract their coefficients.
Step4. Combine the like terms with the new coefficients: Finally, combine the like terms with their new coefficients to get the simplified expression.