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The distributive property is a fundamental rule in algebra that allows us to simplify expressions and solve equations. When faced with an expression involving multiplication over addition or subtraction, you can use the distributive property to break it down into simpler parts.

For example, the distributive property states that:

• For addition: \[ c(a + b) = ca + cb \]
• For subtraction: \[ c(a - b) = ca - cb \]

This means you multiply the number outside the parentheses by each term inside the parentheses.

In the given problem, the expression \[(a-b) 8\]is simplified using the distributive property: \[8(a-b) = 8a - 8b\].

Using this property makes it easier to handle complex expressions and is crucial for solving equations in algebra.

Multiplication is one of the basic operations in mathematics, essential for simplifying and rearranging algebraic expressions. In the context of the distributive property, multiplication comes into play when you distribute a number across terms within parentheses.

When multiplying a number by an expression, each term in the expression needs to be multiplied separately. This operation is straightforward:

• Multiply the number with each term.
• Add or subtract the result based on the operation between the terms.

For example, using the expression \[(a-b)8\],we multiply 8 by each term:

• First, multiply: \[8 \times a = 8a\]
• Then, multiply: \[8 \times (-b) = -8b\]

This process effectively distributes multiplication across the terms inside the parentheses. Mastering multiplication within this context is essential for solving algebraic problems efficiently.

Simplifying expressions is a crucial skill in mathematics that involves breaking down complex expressions into their simplest form. This process often uses the distributive property, as well as other algebraic principles.

When simplifying expressions, the objective is to combine like terms and eliminate unnecessary parentheses, making it easier to work with the expression. Here’s a simple approach:

• Apply the distributive property to remove parentheses.
• Combine like terms where possible.
• Result in a clearer and concise expression.

In the problem at hand, \[(a-b)8\],applying the distributive property yields \[8a - 8b\].There are no like terms to combine further, indicating the expression is fully simplified.

Properly simplifying expressions not only helps in solving problems efficiently but also in understanding the relationship between the components of an equation.