Distributive Property
The distributive property is a fundamental property in mathematics that helps us to simplify expressions and perform operations on algebraic terms
The distributive property is a fundamental property in mathematics that helps us to simplify expressions and perform operations on algebraic terms. It states that when we multiply a number or expression by a sum or difference, we can distribute the multiplication to each term inside the parentheses.
In formal terms, the distributive property states that for any numbers a, b, and c, the following equation holds true:
a * (b + c) = (a * b) + (a * c)
This property can also be applied in reverse. If we have a sum or difference inside parentheses being multiplied by a number or expression, we can apply the distributive property to simplify the expression.
Here’s an example to illustrate the use of the distributive property:
Let’s say we have the expression 3(2x + 4). To simplify this expression using the distributive property, we distribute the multiplication of 3 to each term inside the parentheses:
3(2x + 4) = (3 * 2x) + (3 * 4)
= 6x + 12
In this example, we multiplied each term inside the parentheses, 2x and 4, by 3, resulting in the simplified expression 6x + 12.
The distributive property is extremely useful in algebra as it allows us to simplify complicated expressions, combine like terms, and solve equations more efficiently. It is a foundational concept that is used extensively in higher-level mathematics.
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