What Is Adding Binomials?
To add binomials, group the terms that have the same variable and exponent and add their coefficients. The constants are added together on their own. No signs change in addition, unlike subtraction.
Enter two binomials, plus an optional third, and the calculator returns the combined expression, its degree and its number of terms, with a coefficient table. A value check lets you confirm that the sum of the separate values matches the value of the answer.
Unlike terms stay separate. Adding x² + 3 and 2x + 5 gives x² + 2x + 8, which is a trinomial rather than a binomial.
How to Use the Adding Binomials Calculator
- Enter two binomials, and a third if you need it.
- Read the combined sum.
- Check it at a value if you like.
Adding Binomials Formula
Adding two binomials
Adding Binomials Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| Binomial | A polynomial with two terms | |
| Like terms | Same variable and the same power | |
| Coefficient | The number multiplying the variable | |
| Sum | The combined expression |
Adding Binomials Worked Example
With the example values loaded in the calculator above, the steps are:
- Set up (3x + 5) + (2x - 7) + (x + 4).
- Addition needs no sign changes. Drop the brackets and group the like terms.
- Distribute each term: (3x+5) → 3x + 5; (2x-7) → 2x − 7; (x+4) → x + 4.
- Combine like terms to get 6x + 2.
Result: Sum of 3 binomials = 6x + 2.
Worked example: (3x + 5) + (2x − 7) + (x + 4)
Group like terms: (3x + 2x + x) + (5 − 7 + 4).
The x terms give 6x and the constants give 2, so the sum is 6x + 2.
Unlike terms stay separate
In (x² + 3) + (2x + 5) the terms x² and 2x are not like terms because their exponents differ. The sum is x² + 2x + 8, a trinomial.
Where Adding Binomials Is Used
Algebra homework
Check sums of binomials quickly.
Learning like terms
See how terms are grouped before adding.
Building longer expressions
Combine several binomials before factoring.
Common Adding Binomials Mistakes to Avoid
- Adding never changes the signs. Only subtraction does.
- Keep terms in descending order of power for a tidy answer.
Adding Binomials Terms and Definitions
- Like terms
- Terms with the same variable raised to the same power.
Adding Binomials FAQs
How do you add binomials?
Add the coefficients of the like terms and add the constants.
Can the sum of two binomials be a trinomial?
Yes, when the binomials contain different powers, such as x² + 3 and 2x + 5.
Do I need to change any signs when adding?
No. Sign changes are only needed for subtraction.
Can I add three binomials?
Yes. Use the optional third box.
What if the x terms cancel?
Then the sum has fewer terms, for example (x + 3) + (−x + 5) = 8.
How can I check my answer?
Evaluate each binomial and the sum at the same number. The values must add up.