Simplifying Algebraic Expressions
To simplify algebraic expressions, you need to follow a few steps:
1. Combine like terms: Look for terms that have the same variables with the same exponents. You can add or subtract them accordingly. For example, in the expression 3x + 2x, you can combine the x terms to get 5x.
2. Apply the distributive property: If you have terms inside parentheses that need to be multiplied by a common factor, distribute the factor to each term. For example, in the expression 2(x + 3), distribute the 2 to get 2x + 6.
3. Remove parentheses: If you have parentheses in your expression, remove them by applying the distributive property or by combining like terms. For example, in the expression (3x + 2) + (4x - 1), you can remove the parentheses by combining like terms inside each set of parentheses and then combining the resulting terms outside the parentheses.
4. Simplify further: Once you have combined like terms, distributed factors, and removed parentheses, check if there are any additional simplification steps you can take, such as factoring, canceling common factors, or combining similar terms.
Here are a few examples to illustrate these steps:
Example 1:
Simplify the expression 4x + 2 - 3x + 5x - 1.
- Combine like terms: 4x - 3x + 5x = 6x.
- Combine the constant terms: 2 - 1 = 1.
So, the simplified expression is 6x + 1.
Example 2:
Simplify the expression 3(x + 2) - 2(2x - 1).
- Apply the distributive property: 3(x + 2) = 3x + 6 and -2(2x - 1) = -4x + 2.
- Remove parentheses: 3x + 6 - 4x + 2.
- Combine like terms: 3x - 4x = -x and 6 + 2 = 8.
So, the simplified expression is -x + 8.
By following these steps, you can simplify algebraic expressions effectively.