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Simplifying expressions is the process of making algebraic expressions easier to work with by combining like terms and applying mathematical operations. In basic algebra, this often involves operations such as addition, subtraction, multiplication, and division. When simplifying expressions, the goal is to rewrite the expression in its simplest form.

For example, consider the expression given in the exercise: \(7(x + 9)\). By applying the distributive property, we can simplify this expression to make it easier to understand and work with.

To simplify an expression using the distributive property, follow these steps:

• Identify the terms inside the parentheses.
• Apply the distributive property to multiply each term inside the parentheses by the factor outside.
• Combine the resulting terms if possible.

Algebraic multiplication involves multiplying coefficients and variables according to the rules of algebra. This often includes applying properties such as the distributive property to expand expressions and combine like terms. The distributive property is particularly useful in algebraic multiplication when dealing with expressions that include parentheses.

For instance, in the exercise \(7(x + 9)\), algebraic multiplication is used to distribute the 7 through the terms inside the parentheses. This can be broken down as follows:

• Multiplying 7 by \(x\) to get \(7x\).
• Multiplying 7 by 9 to get 63.

By performing these multiplications step by step, we ensure accuracy and simplify the initial expression.

Basic algebra lays the foundation for understanding more complex mathematical concepts by introducing variables, constants, and basic operations. One of the key principles in basic algebra is learning how to manipulate and simplify expressions. This exercise highlights the use of the distributive property, an essential algebraic property.

The distributive property helps to simplify expressions where a single term is multiplied by a sum or difference inside parentheses. This property is written as \(a(b + c) = ab + ac\).

In the context of basic algebra, understanding the distributive property allows students to break down more complex expressions into simpler parts, making them easier to solve. For example, the expression \(7(x + 9)\) can be simplified to \(7x + 63\) by applying the distributive property, demonstrating how a seemingly complicated expression can be handled using basic algebraic rules.