Simplify Expression Calculator
Simplify algebraic expressions by combining like terms with step-by-step solutions
Use variables like x, y, z with coefficients and constants
How to Simplify Algebraic Expressions
Simplifying algebraic expressions means rewriting them in their simplest form by combining like terms, removing parentheses, and organizing terms in standard order.
Steps to Simplify Expressions
- Remove Parentheses: Apply the distributive property if needed
- Identify Like Terms: Terms with the same variables and exponents
- Combine Like Terms: Add or subtract coefficients of like terms
- Arrange in Standard Form: Highest degree terms first, then constants
What Are Like Terms?
Like terms have identical variable parts:
- 3x and 5x are like terms (both have x)
- 2x² and 7x² are like terms (both have x²)
- 3x and 5y are NOT like terms (different variables)
- 2x and 4x² are NOT like terms (different exponents)
Example
Simplify: 2x + 3x - 5 + 2
- Group like terms: (2x + 3x) + (-5 + 2)
- Combine x terms: 5x
- Combine constants: -3
- Final answer: 5x - 3
Frequently Asked Questions
What does it mean to simplify an expression?
Simplifying an expression means rewriting it in the most concise form possible by combining like terms and performing any possible operations, while maintaining the same mathematical value.
How do I identify like terms?
Like terms have exactly the same variable part, including the same exponents. Only the coefficients can be different. For example, 3x² and -5x² are like terms, but 3x² and 3x are not.
Can I combine x and x²?
No, x and x² are not like terms because they have different exponents. You can only combine terms that have identical variable parts, including the same exponents.
What is standard form for an expression?
Standard form arranges terms from highest degree to lowest, then includes the constant term last. For example: 3x² + 2x - 5 is in standard form.
Why do we simplify expressions?
Simplifying makes expressions easier to work with, easier to evaluate, and easier to compare. It's also necessary before solving equations or performing further algebraic operations.
What if there are parentheses in the expression?
First apply the distributive property to remove parentheses, then identify and combine like terms. Always work from the innermost parentheses outward if there are nested parentheses.
Can expressions with different variables be simplified?
Yes, you can simplify by combining like terms of each variable separately. Terms with different variables cannot be combined with each other.
What about negative coefficients?
Treat negative coefficients just like positive ones when combining like terms. For example, 5x + (-3x) = 5x - 3x = 2x. Be careful with signs when adding and subtracting.
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