Evaluate Expression Calculator
Evaluate algebraic expressions with multiple variables at given values
Use ^ for exponents (e.g., x^2 for x squared)
How to Evaluate Expressions
Evaluating an expression means finding its numerical value when specific values are substituted for the variables. This is a fundamental skill in algebra used in many real-world applications.
Steps to Evaluate an Expression
- Write down the original expression clearly
- Identify all variables and their given values
- Substitute each variable with its value (use parentheses)
- Simplify using order of operations (PEMDAS)
- Calculate the final numerical result
Order of Operations (PEMDAS)
- Parentheses - Evaluate expressions inside parentheses first
- Exponents - Calculate powers and roots
- Multiplication and Division - Left to right
- Addition and Subtraction - Left to right
Example
Evaluate 2x² + 3xy - y² when x = 3 and y = 2:
- = 2(3)² + 3(3)(2) - (2)²
- = 2(9) + 3(3)(2) - 4
- = 18 + 18 - 4
- = 32
Common Applications
- Physics formulas (distance, velocity, force)
- Financial calculations (interest, profit, cost)
- Engineering equations
- Scientific research and data analysis
Frequently Asked Questions
What does it mean to evaluate an expression?
Evaluating an expression means finding its numerical value by substituting specific numbers for the variables and then calculating the result using the order of operations.
Why use parentheses when substituting?
Parentheses ensure the correct calculation, especially with negative numbers, exponents, or coefficients. For example, 2x² when x = -3 should be 2(-3)² = 2(9) = 18, not 2(-3²) = -18.
What if my expression has multiple occurrences of the same variable?
Substitute the same value everywhere that variable appears. For example, in x² + 3x when x = 2, substitute 2 for both x's: (2)² + 3(2) = 4 + 6 = 10.
Can I evaluate expressions with fractions or decimals?
Yes! Variables can take any real number values, including fractions and decimals. Just substitute them the same way and calculate carefully.
What happens with negative variable values?
Always put negative values in parentheses when substituting. This prevents sign errors, especially with exponents. For example, x² when x = -2 is (-2)² = 4, not -4.
How do I handle exponents when evaluating?
Calculate exponents after substitution but before multiplication. Follow PEMDAS: parentheses first, then exponents, then multiplication/division, and finally addition/subtraction.
What if I get a different answer than expected?
Double-check your substitution (especially signs and parentheses), verify you followed PEMDAS correctly, and make sure you calculated exponents before other operations.
Can expressions have more than two variables?
Absolutely! Expressions can have any number of variables. Just substitute each variable with its given value and evaluate following the order of operations.
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