Distributive Property Calculator
Apply the distributive property a(b + c) = ab + ac with step-by-step solutions
Use format: a(b + c) or a(b - c)
Examples to try:
• 3(2x + 5) → Positive coefficient
• -2(3a - 4b) → Negative coefficient
• 5(x + 7) → Single variable
• -1(4y - 9) → Coefficient of -1
Understanding the Distributive Property
The distributive property is a fundamental algebraic property that allows you to multiply a single term by each term inside parentheses. It's essential for simplifying expressions and solving equations.
The Distributive Property Formula
a(b + c) = ab + ac
a(b - c) = ab - ac
How to Apply the Distributive Property
- Identify the term outside the parentheses (the multiplier)
- Multiply this term by the first term inside the parentheses
- Multiply the same term by the second term inside the parentheses
- Keep the operation sign between the results
- Simplify if possible by combining like terms
Working with Negative Numbers
When distributing a negative number, the signs of all terms inside change:
-2(3x - 4) = -2(3x) + (-2)(-4) = -6x + 8
Examples
Example 1: Positive coefficient
- 3(2x + 5)
- = 3(2x) + 3(5)
- = 6x + 15
Example 2: Negative coefficient
- -2(3a - 4b)
- = -2(3a) + (-2)(-4b)
- = -6a + 8b
Frequently Asked Questions
What is the distributive property?
The distributive property states that a(b + c) = ab + ac. It allows you to multiply a number or variable outside parentheses by each term inside the parentheses separately.
Why is it called "distributive"?
It's called distributive because you distribute (or spread out) the multiplication over addition or subtraction. The outside term is multiplied to each term inside the parentheses.
What happens when distributing a negative number?
When you distribute a negative number, multiply it by each term inside. Remember that negative times positive is negative, and negative times negative is positive. For example, -2(3 - 4) = -6 + 8.
Can I use the distributive property in reverse?
Yes! This is called factoring. You can go from ab + ac back to a(b + c) by finding the common factor. This is the reverse of distribution.
Does the distributive property work with subtraction?
Yes! The distributive property works with subtraction: a(b - c) = ab - ac. You distribute the multiplication over the subtraction operation.
What if there are more than two terms inside parentheses?
The distributive property extends to any number of terms. For a(b + c + d), you multiply a by each term: ab + ac + ad.
Can variables be distributed over other variables?
Yes! For example, x(y + z) = xy + xz. The distributive property works with any terms, whether they're numbers, variables, or combinations of both.
When should I use the distributive property?
Use it when simplifying expressions with parentheses, solving equations, multiplying polynomials, or when you need to combine like terms that are separated by parentheses.
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