Distributive Property of Multiplication over Subtraction

The distributive property of multiplication over subtraction is a fundamental property in mathematics that allows us to simplify expressions involving both multiplication and subtraction. It states that when we multiply a number or term by the difference of two other numbers or terms, we can distribute the multiplication to each term within the difference individually.

Explanation

To understand the distributive property of multiplication over subtraction, let's consider the following expression:

a * (b - c)

According to the distributive property, we can rewrite this expression as:

(a * b) - (a * c)

This means that we can multiply the number or term 'a' by each term within the parentheses individually and then subtract the results. It provides a way to simplify the expression and perform the multiplication and subtraction operations separately.

Example:
Let's take a numerical example to illustrate the distributive property:

3 * (8 - 2)

Using the distributive property, we can rewrite this expression as:

(3 * 8) - (3 * 2)

Simplifying further, we get:

24 - 6 = 18

Therefore, the result of the expression 3 * (8 - 2) is 18.

Key Points:
- The distributive property of multiplication over subtraction allows us to distribute the multiplication operation to each term within the difference individually.
- It helps in simplifying expressions involving both multiplication and subtraction.
- The property can be applied to both numerical values and algebraic terms.
- When using the distributive property, we can perform multiplication and subtraction operations separately, which makes it easier to calculate the final result.

Conclusion

The distributive property of multiplication over subtraction is a useful tool in simplifying expressions involving both multiplication and subtraction. It allows us to distribute the multiplication operation to each term within the difference individually, making it easier to perform the calculations. By applying this property, we can simplify complex expressions and obtain the final result more efficiently.