What Is Add and Subtract Binomials?
A binomial is a polynomial with two terms, such as 3x + 5. To add two binomials you add the coefficients of the like terms. To subtract, you first change the sign of every term in the second binomial, then add.
Enter binomial A, choose add or subtract, and enter binomial B. The calculator shows the setup, the sign change when you subtract, the combined result and a coefficient table, with an optional check at a chosen value.
Terms can cancel. Subtracting (3x + 5) − (3x − 2) leaves just 7, so the answer is not always a binomial.
How to Use the Add and Subtract Binomials Calculator
- Enter the first and second binomial.
- Choose add or subtract.
- Read the combined result and the step that shows the sign change.
Add and Subtract Binomials Formula
Addition
Subtraction
Add and Subtract Binomials Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| A | The first binomial | e.g. 3x + 5 |
| B | The second binomial | e.g. 2x − 7 |
| Like terms | Terms with the same variable and exponent | |
| Coefficient | The number in front of a variable |
Add and Subtract Binomials Worked Example
With the example values loaded in the calculator above, the steps are:
- Set up (3x + 5) − (2x - 7).
- Subtracting changes the sign of every term in the second binomial.
- Distribute each term: (3x+5) → 3x + 5; -(2x-7) → −2x + 7.
- Combine like terms to get x + 12.
Result: Difference (A − B) = x + 12.
Worked example: (3x + 5) − (2x − 7)
Change the signs of the second binomial: 3x + 5 − 2x + 7.
Combine like terms: 3x − 2x = x and 5 + 7 = 12. The result is x + 12.
Is the answer still a binomial?
Not always. If the x terms cancel, such as (3x + 5) − (3x − 2), the answer is the single number 7. The calculator shows the number of terms so you can see this.
Where Add and Subtract Binomials Is Used
Checking homework
Compare your combined result with the calculator.
Learning sign rules
See exactly how subtraction flips the second binomial.
Building bigger expressions
Combine binomials before factoring or solving.
Common Add and Subtract Binomials Mistakes to Avoid
- Treat subtraction as adding the opposite of every term.
- Only combine terms with the same variable and exponent.
Add and Subtract Binomials Terms and Definitions
- Binomial
- A polynomial with exactly two terms, such as 3x + 5.
Add and Subtract Binomials FAQs
How do you add binomials?
Add the coefficients of like terms: x terms with x terms and constants with constants.
How do you subtract binomials?
Distribute the minus sign across the second binomial, flipping both signs, then combine like terms.
Can the result have fewer than two terms?
Yes, terms can cancel, leaving one term or just a number.
Can I use binomials with squared terms?
Yes, such as x² + 3 and 2x² − 1. Like terms are matched by exponent.
What is the difference between a binomial and a polynomial?
A binomial is a polynomial with two terms. Polynomials can have any number of terms.
Why check with a value?
Substituting a number into A − B and into your answer should give the same result.