Expressions describe; equations assert equality
An expression combines values and operations without claiming that it equals something else. An equation connects two expressions with an equals sign. You simplify an expression; you solve an equation for values that make it true.
In 7x² − 3x + 8, x is the variable, 7 and −3 are coefficients, and 8 is a constant term. The sign belongs with its term.
Combine only like terms
Like terms have identical variable parts, including powers. You can combine 4x² with −x², but not with 4x. Think of the variable part as a label and combine its coefficients.
When substituting a value, use parentheses around negative numbers. For x = −2, x² is 4 while −x² is −4. The position of the minus sign matters.
Know what the tool accepts
The polynomial tool accepts expanded expressions in x. Distribute brackets by hand before entering them, or enter the two factors separately and select Multiply. It is not a general symbolic interpreter.
After simplifying, evaluate the old and new expressions at a small value such as x = 2. Matching results are a useful spot check, though one matching point alone does not prove an identity.
LET’S WORK IT THROUGH
Simplify 4x² + 3x − x² + 5x − 6.
- Collect squared terms: 4x² − x² = 3x².
- Collect linear terms: 3x + 5x = 8x.
- Keep the constant −6.
THE ANSWER3x² + 8x − 6.
YOUR TURN
A small check for understanding.
Evaluate 2x² − 3 at x = −2.
Reveal the answer
5. Square −2 first to get 4, multiply by 2, then subtract 3.
Now try your own numbers.
The polynomial calculator includes input guidance and the limits of its supported calculations. Use it alongside the method above.
Open Polynomial calculator ↗A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.