What Is Distribution Algebra?
The distributive property says a(b + c) = ab + ac. It is the basis for expanding brackets and multiplying polynomials: multiply each term of one factor across the other, then combine like terms.
Enter each expression as coefficients from the highest power down. The calculator shows each term being distributed, the expanded product and a numeric check that substitutes a value into both forms.
Below are the rules, a worked example with a trinomial and answers on negatives and checking.
How to Use the Distribution Algebra Calculator
- Enter each expression as coefficients.
- Read every distribution step.
- Check the expanded product.
- Confirm with the numeric check.
Distribution Algebra Formula
Distributive property
Two binomials
Distribution Algebra Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| k | Multiplier outside the brackets | |
| a, b, c | Terms or coefficients inside | |
| Like terms | Same variable and exponent | |
| Degree | Highest power in the product |
Distribution Algebra Worked Example
Expand 3(2x² − 5x + 4). Multiply 3 by each term: 3·2x² = 6x², 3·(−5x) = −15x and 3·4 = 12. The result is 6x² − 15x + 12. At x = 2 the original gives 3 × (8 − 10 + 4) = 6 and the result gives 24 − 30 + 12 = 6.
With the example values loaded in the calculator above, the steps are:
- Write the expressions: (3) × (2x² − 5x + 4).
- Distribute 3: 3 × (2x² − 5x + 4) = 6x² − 15x + 12.
- Add like terms: 6x² − 15x + 12.
Result: Expanded product = 6x² − 15x + 12.
How to Read the Expanded Product
Distribution multiplies every term of the first expression by every term of the second, then combines like terms. For 3(2x² − 5x + 4) the result is 6x² − 15x + 12.
The check value helps you catch slips. At x = 2 the original gives 3 × (8 − 10 + 4) = 6 and the result gives 24 − 30 + 12 = 6. If the two numbers differ, one step went wrong.
Where Distribution Algebra Is Used
Expanding brackets
Multiply a number or a polynomial across a bracket and combine like terms.
Negative factors
See what happens to every sign when you distribute a negative number.
Polynomial products
Multiply two polynomials with a full term-by-term expansion.
Checking homework
Use the check value to test your own answer before you hand it in.
Common Distribution Algebra Mistakes to Avoid
- Distribute to every term in the bracket, including the last one. A forgotten term is the usual error.
- A negative outside the bracket changes every sign inside it.
- Combine like terms only after you have multiplied everything.
- Test the answer with a number. If both forms give the same value, the expansion is very likely right.
Distribution Algebra Terms and Definitions
- Like terms
- Terms with the same variable and exponent.
Distribution Algebra FAQs
What is the distributive property?
It says a(b + c) = ab + ac. You multiply the outside factor by each term inside the bracket and add the results.
How do you distribute a negative number?
Multiply each term by the negative, which flips its sign. −2(x − 3) = −2x + 6, because −2 × −3 is positive.
How do you multiply two polynomials?
Multiply each term of the first by each term of the second, then add like terms. (x + 2)(x + 3) = x² + 3x + 2x + 6 = x² + 5x + 6.
How can I check my answer?
Substitute a simple number for the variable into both the original and the expanded form. They must give the same value, as in the check value shown by the calculator.