September 29, 2025

What Is The Distributive Property

Q: Does the distributive property work with division?

Yes, but only when the sum or difference is being divided (the dividend). For example, (8 + 4) ÷ 2 = (8 ÷ 2) + (4 ÷ 2). However, it does not work when the number is being divided by a sum, so 12 ÷ (2 + 4) is not equal to (12 ÷ 2) + (12 ÷ 4).

Q: What is the difference between the distributive and commutative properties?

The distributive property involves two different operations (e.g., multiplication and addition), like a(b + c) = ab + ac. The commutative property involves only one operation and states that the order of the numbers does not change the result, such as a + b = b + a or a × b = b × a.

Q: Can you use the distributive property with more than two terms?

Absolutely. The property applies to any number of terms within the parentheses. For example, 5(x + y - z) would be distributed to all three terms, resulting in 5x + 5y - 5z.

Q: Is factoring the same as the distributive property?

Factoring is essentially the reverse of the distributive property. While distribution involves multiplying a factor into a group of terms (e.g., 2(x+3) becomes 2x+6), factoring involves finding a common factor and pulling it out (e.g., 2x+6 becomes 2(x+3)).

Learn the definition of the distributive property, a fundamental rule in algebra that allows you to multiply a single term by two or more terms inside a set of parentheses.

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Defining the Distributive Property

The distributive property is a fundamental rule in algebra that states that multiplying a sum by a number is the same as multiplying each addend in the sum by the number and then adding the products. In simple terms, it allows you to 'distribute' a factor to each term within a parenthesis.

Section 2: The Formula

The property is most commonly expressed with the formula a(b + c) = ab + ac. This shows that the term 'a' outside the parentheses is distributed to both 'b' and 'c' inside the parentheses through multiplication. The same principle applies to subtraction: a(b - c) = ab - ac.

Section 3: A Practical Example

Consider the expression 4(5 + 2). Using the distributive property, you multiply 4 by each term inside the parentheses: (4 × 5) + (4 × 2). This simplifies to 20 + 8, which equals 28. You can verify this by first adding the terms in the parentheses (5 + 2 = 7) and then multiplying by 4 (4 × 7 = 28), yielding the same result.

Section 4: Why Is It Important?

The distributive property is crucial for simplifying algebraic expressions, solving equations, and factoring polynomials. It provides a method for handling expressions with variables that cannot be combined first, such as 3(x + 5), which simplifies to 3x + 15. Mastering this property is essential for success in algebra and higher-level mathematics.

Frequently Asked Questions

Does the distributive property work with division?

What is the difference between the distributive and commutative properties?

Can you use the distributive property with more than two terms?

Is factoring the same as the distributive property?