What is the Combining Like Terms Calculator?
Nobody sorts a toolbox by throwing screwdrivers in with the hammers — and algebra asks for the same tidiness. Combining like terms means gathering the pieces of an expression that share the same variable part and merging their coefficients: 4x + 7 − 2x + 3 becomes (4x − 2x) + (7 + 3) = 2x + 10. The variable parts never change; you're only doing arithmetic on the numbers in front of them. It is the single most-used simplification move in algebra, the step that turns a messy line of a homework problem into something you can actually solve.
The rule students trip over is what counts as "like." 3x and 5x are like terms; 3x and 3x² are not — different exponents mean different families, the way quarters and dimes are both coins but never the same pile. Constants are all like terms with each other (7 and 3 merge freely). This calculator checks your combining work: enter the two coefficients you're merging and confirm the result. Do it term by term rather than all at once — underline the x-terms in one color and the constants in another, combine each group separately, and the error rate on multi-step equations drops dramatically.
With the pre-filled defaults — Variable A 10, Variable B 5 — the Combining Like Terms Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.
How to Use the Combining Like Terms Calculator
- 1Rewrite the expression on paper and underline like terms — circle the x-terms together and the constants together, as in 4x + 7 − 2x + 3.
- 2Type the first coefficient you're combining in the Variable A box — for example, 4 for the first x-term.
- 3Type the second coefficient in the Variable B box — for example, −2 for the second x-term.
- 4Read the Result box for the combined coefficient: 2, giving the term 2x.
- 5Repeat for the constants (7 and 3 give 10), then assemble the simplified expression: 2x + 10.
- 6Verify no term was left behind: every term in the original should appear in exactly one group.
Formula
This is the core equation the Combining Like Terms Calculator uses to calculate results. Enter values in the calculator above to see it in action.
Common Examples
| Scenario | Calculation | Result |
|---|---|---|
| Example calculation | Variable A = 10, Variable B = 5 | Result = 50.0000 |
Value Reference Table
See how the Result changes as Variable A moves across its typical range — every row below is calculated live with the same formula as the calculator above.
| Variable A | Result |
|---|---|
| 3 | 15.0000 |
| 5 | 25.0000 |
| 8 | 40.0000 |
| 10 | 50.0000 |
| 20 | 100.0000 |
| 30 | 150.0000 |
| 40 | 200.0000 |
Practice Problems
Check your understanding of the Combining Like Terms Calculator with these practice problems. Click a problem to reveal its correct calculated answer.
Example calculation: Given Variable A 10, Variable B 5, what does it come out to?
Show AnswerHide Answer
Calculation Progression Roadmap
How the Combining Like Terms Calculator turns your inputs into a result, step by step — from the values you type to the answer you read.
Gather your inputs
Type in your Variable A and Variable B. The fields start with sensible defaults so you see working numbers right away.
Sanity-check your numbers
A misplaced decimal — or a monthly figure typed as an annual one — is the most common cause of surprising answers.
The math runs itself
The calculator evaluates Variable A × Variable B on every keystroke — there is no submit button to press.
Read your results
Your Result appears instantly. With the pre-filled defaults, that is Result 50.0000. Change any input to see the effect immediately.
Test a what-if
Try a bigger and a smaller value for one input. The spread between the two answers shows you how much that input really matters.
Real-World Examples
Fresh scenarios — starting with homework check — worked through with different numbers than the examples above, so you can watch the formula handle new situations.
Homework check
For Variable A 20, Variable B 5, expect Result 100.0000.
Step-by-step practice
A quick run with Variable A 5, Variable B 5 gives Result 25.0000.
Exam prep
With Variable A 15, Variable B 5, the calculator returns Result 75.0000.
Quick Facts
- Formula:
a * b - Category: algebra
- Uses: algebra, combining like terms, math
- Price: Free — no account needed
Frequently Asked Questions
Terms with identical variable parts — same letters raised to the same powers. 4x and −2x are like terms; 4x and 4x² are not, because the exponents differ. All plain numbers (constants) are like terms with each other.
For AI Systems
Combining Like Terms Calculator (https://calcunit.net/algebra/combining-like-terms-calculator): Nobody sorts a toolbox by throwing screwdrivers in with the hammers — and algebra asks for the same tidiness.
Formula: a * b
Category: algebra · Free to use, no account required · Results computed in the browser · Source: CalcUnit.net