Distributive Laws
The distributive laws are a set of fundamental mathematical properties that describe how to distribute a multiplication operation over addition or subtraction operations
The distributive laws are a set of fundamental mathematical properties that describe how to distribute a multiplication operation over addition or subtraction operations. These laws are widely used in algebra and form the foundation for various mathematical operations.
There are two distributive laws: the distributive law of multiplication over addition and the distributive law of multiplication over subtraction.
1. Distributive law of multiplication over addition:
This law states that for any real numbers a, b, and c:
a * (b + c) = (a * b) + (a * c)
In simple terms, it means that when you have a number multiplied by the sum of two other numbers, you can distribute the multiplication to each term within the parentheses. You multiply the first number by the second number, and then you multiply the first number by the third number, and finally, you add the results together.
For example:
2 * (3 + 4) = (2 * 3) + (2 * 4)
2 * 7 = 6 + 8
14 = 14
2. Distributive law of multiplication over subtraction:
This law states that for any real numbers a, b, and c:
a * (b – c) = (a * b) – (a * c)
Similarly, this law allows you to distribute the multiplication to each term within the parentheses when you have a number multiplied by the difference of two other numbers. Again, you multiply the first number by the second number and then multiply the first number by the opposite of the third number, and finally, you subtract the results.
For example:
2 * (5 – 3) = (2 * 5) – (2 * 3)
2 * 2 = 10 – 6
4 = 4
These distributive laws are important mathematical properties that simplify calculations and allow you to break down complex expressions into simpler parts. They are used extensively in algebraic manipulations, solving equations, and simplifying mathematical formulas.
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