The Distributive Property
The distributive property in math allows you to simplify expressions by distributing a factor to each term within parentheses. In simpler terms, it means you can multiply a number outside the parentheses by each number inside the parentheses and then add the results.
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The Concept:
When you have a number (or variable) multiplying a sum or difference within parentheses, the distributive property lets you "distribute" that number to each term inside the parentheses.
This means you multiply the number outside by each term inside separately, then add (or subtract) the results.
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The Formula:
The distributive property is often written as: a * (b + c) = (a * b) + (a * c)
It also applies to subtraction: a * (b - c) = (a * b) - (a * c)
Where 'a', 'b', and 'c' can be numbers or variables.
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Example:
Let's say you have the expression 3 * (4 + 2).
Using the distributive property:
3 * (4 + 2) = (3 * 4) + (3 * 2)
= 12 + 6
= 18
This is the same as first adding inside the parentheses (4 + 2 = 6) and then multiplying (3 * 6 = 18).
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Why is it useful?
The distributive property helps simplify expressions, especially when terms inside parentheses cannot be combined (e.g., when they involve variables).
It's a fundamental concept used in algebra to solve equations and simplify expressions.
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