Distributive property is a fundamental concept in mathematics that describes how multiplication distributes over addition or subtraction. It allows us to simplify expressions by breaking them down into smaller, more manageable parts. The distributive property states that for any three numbers a, b, and c:

a(b + c) = ab + ac

In other words, when we multiply a number by the sum of two other numbers, we can distribute the multiplication to each term inside the parentheses.

Using the distributive property, we can simplify expressions and make calculations easier. Let's take a closer look at the example you provided:

4(4 + 6)

This expression represents multiplying 4 by the sum of 4 and 6. To apply the distributive property, we can distribute the multiplication to each term inside the parentheses:

4 * 4 + 4 * 6

Simplifying further, we have:

16 + 24

Which gives us the final answer of:

40

Therefore, the expression 4(4 + 6) is equal to 40.

Let's summarize the steps taken to apply the distributive property in this example:

1. Recognize the expression and identify the terms involved.
2. Identify the operation being performed (multiplication in this case).
3. Apply the distributive property by distributing the multiplication to each term inside the parentheses.
4. Simplify the expression by performing the multiplication and addition/subtraction.
5. Obtain the final answer.

The distributive property is a versatile tool that can be used in various mathematical operations, such as multiplying polynomials, simplifying algebraic expressions, and solving equations. It is an essential concept to understand and apply in order to solve mathematical problems efficiently.

By utilizing the distributive property, we can break down complex expressions into simpler ones, making calculations more manageable and providing a solid foundation for further mathematical concepts.