Distributive Property
The sum of two addends multiplied by a number is the sum of the product of each addend and the number.
The distributive property is a mathematical property that is used to simplify expressions by distributing or multiplying a factor to every term inside a parenthesis. It is a fundamental property of algebra that helps to solve equations, simplify expressions, and factor polynomials.
The distributive property is usually written as:
a(b + c) = ab + ac or
a(b – c) = ab – ac
Where a, b, and c are any real numbers.
This property states that when we multiply a factor (a in this case) to a set of parenthesis containing two or more terms, we can multiply the factor by every term inside the parenthesis separately and then add or subtract the resulting products to get the final expression.
For example, consider the expression 4(x + 3), where we have a factor of 4 and a set of parenthesis containing two terms (x and 3). Applying the distributive property, we get:
4(x + 3) = 4x + 4(3)
= 4x + 12
Here, we first multiply the factor 4 to the first term inside the parenthesis (x) and get 4x. Then, we multiply the same factor with the second term (3) and get 4(3) = 12. Finally, we add these two products to get 4x + 12, which is the simplified expression.
The distributive property is a powerful tool in algebra and is used extensively in solving equations, simplifying expressions, and factorizing polynomials. It is also the basis of the foil method used to expand binomial expressions and is an essential concept for students to master in algebra.
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