The distributive property is a fundamental property in mathematics that governs how multiplication and addition (or subtraction) interact with each other. It is commonly used to simplify algebraic expressions and to perform arithmetic operations more efficiently. The distributive property states that:
For any three numbers, a, b, and c:
Multiplication distributes over addition:
a * (b + c) = a * b + a * c
Multiplication distributes over subtraction:
a * (b - c) = a * b - a * c
In words, the distributive property tells us that when we have a number (a) multiplied by the sum or difference of two other numbers (b and c), we can distribute the multiplication to each term inside the parentheses. We multiply a by b and also multiply a by c, and then add or subtract the results.
For example:
2 * (3 + 4) = 2 * 3 + 2 * 4
2 * 7 = 6 + 8
14 = 14
5 * (2 - 1) = 5 * 2 - 5 * 1
5 * 1 = 10 - 5
5 = 5
The distributive property can be extended to more than two terms inside the parentheses as well. It is a fundamental concept in algebra and plays a crucial role in solving equations, factoring polynomials, and simplifying expressions.
I hope this helped!
~~~Harsha~~~