What Is Simplify Expressions with Distribution?
To simplify an expression with distribution, you multiply the factor outside a bracket by each term inside it, then add or subtract the like terms. The rule is a(b + c) = ab + ac, and it also works for products of two brackets.
Type an expression such as 3(2x + 5) − 2(x − 4). The calculator shows each top-level term expanded on its own, then the combined result, the degree and the number of terms. You can also evaluate the answer at a value to check your own working.
The step most people get wrong is the sign. A minus in front of a bracket flips every term inside, so −2(x − 4) becomes −2x + 8, not −2x − 8.
How to Use the Simplify Expressions with Distribution Calculator
- Type the expression with its brackets.
- Check the step line to see each bracket distributed.
- Read the simplified result, and optionally evaluate it at a value to check your own work.
Simplify Expressions with Distribution Formula
Distributive property
Subtracting a bracket
Simplify Expressions with Distribution Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| a(b + c) | A factor outside a bracket | |
| Like terms | Terms with the same variable and power | 6x and −2x are like terms |
| Coefficient | The number multiplying a variable | |
| Degree | The highest power of the variable |
Simplify Expressions with Distribution Worked Example
With the example values loaded in the calculator above, the steps are:
- Distribute each term: 3(2x+5) → 6x + 15; -2(x-4) → −2x + 8.
- Combine like terms to get 4x + 23.
Result: Simplified expression = 4x + 23.
Worked example: 3(2x + 5) − 2(x − 4)
Distribute 3: 3(2x + 5) = 6x + 15. Distribute −2: −2(x − 4) = −2x + 8.
Combine like terms: 6x − 2x = 4x and 15 + 8 = 23. The simplified expression is 4x + 23. At x = 2 both forms equal 31.
Where Simplify Expressions with Distribution Is Used
Algebra homework
Check your distribution and your combining of like terms.
Preparing to solve equations
Simplify both sides before isolating the variable.
Spotting sign errors
Evaluate the original and simplified form at the same number to confirm they match.
Common Simplify Expressions with Distribution Mistakes to Avoid
- Always distribute before combining, and keep brackets until you have multiplied through.
- Check by substituting a number into both the original and the answer.
Simplify Expressions with Distribution Terms and Definitions
- Like terms
- Terms with the same variable and exponent, such as 6x and −2x.
- Coefficient
- The number multiplying a variable.
Simplify Expressions with Distribution FAQs
What is the distributive property?
It lets you multiply a sum by a number by multiplying each part: a(b + c) = ab + ac.
How do I distribute a negative number?
Multiply every term inside the bracket by the negative number, which flips each sign.
What are like terms?
Terms with the same variable raised to the same power. Only like terms can be added or subtracted.
Can I use fractions or decimals?
Yes. Decimals are converted to exact fractions. For fractions type 1/2, and note that 1/2x means (1/2)x.
Does it handle two brackets multiplied together?
Yes. (x + 2)(x − 3) is expanded fully to x² − x − 6.
Why check by substituting a number?
If the original and simplified expressions give the same value for a test number, the simplification is very likely correct.