Which equation exemplifies the distributive law? A) (a + b) + c = a + (b + c) B) a × (b + c) = a × b + a × c C) a + b = b + a D) a × b = b × a
Understand the Problem
The question is asking which equation demonstrates the distributive law in mathematics. This law states that a single term multiplied by a sum of terms is equal to the sum of each term multiplied by that single term.
Answer
$$ a(b + c) = ab + ac $$
Answer for screen readers
The equation that demonstrates the distributive law is typically in the form of $$ a(b + c) = ab + ac $$.
Steps to Solve
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Identify the distributive law The distributive law can be stated as: $$ a(b + c) = ab + ac $$ Here, $a$ is the single term, and $b$ and $c$ are terms in the sum.
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Examine possible equations Look at each provided equation and see if it matches the form of the distributive law. This involves checking if there is a single term being multiplied by a sum of terms, which are then separated into individual products.
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Select the equation that applies From the options you have, the one that accurately represents the distributive law would be the equation that fits the pattern of distributing the single term across the sum.
The equation that demonstrates the distributive law is typically in the form of $$ a(b + c) = ab + ac $$.
More Information
The distributive law is a foundational concept in algebra that helps simplify expressions and solve equations. It shows how multiplication distributes over addition and is used extensively in both pure and applied mathematics.
Tips
- Confusing the distributive law with other properties of operations like associative or commutative laws.
- Failing to properly distribute the term across all terms in the sum.
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