Problem 27 - Algebra A Combined Function

Question

Simplify each expression. Use the distributive property to remove any parentheses. $$ -2(x+2) $$

Step-by-Step Solution

Answer

The simplified expression is \(-2x - 4\).

Step 1: Identify Parts of the Expression

The expression is \[-2(x+2)\].It contains a scalar \(-2\) and a binomial \((x+2)\) within parentheses. We will apply the distributive property to remove the parentheses.

Step 2: Apply the Distributive Property

The distributive property states that \(a(b + c) = ab + ac\).Here, we need to multiply \(-2\) by each term inside the parentheses. This gives us:\[-2 \times x + (-2) \times 2\].

Step 3: Perform the Multiplication

Calculate each multiplication:\(-2 \times x = -2x\) and \(-2 \times 2 = -4\).

Step 4: Write the Simplified Expression

Combine the results from Step 3 to form the simplified expression:\(-2x - 4\).

Key Concepts

Simplifying Expressions

Simplifying expressions is a fundamental skill in algebra that involves rewriting expressions in a more compact or efficient form without changing their value. It often makes complex expressions easier to understand and work with.To simplify an expression, you can start by eliminating parentheses using operations like distribution or combining like terms. In our example \(-2(x+2)\), we use the distributive property to simplify. Breaking down the steps helps to clarify the process of simplification.By applying the distributive property, we eliminate the parentheses and arrive at a simpler form, \(-2x-4\). This expression is easier to interpret and can be used in further calculations or evaluations.

Binomial Multiplication

Binomial multiplication involves expanding expressions where two terms, known as binomials, are multiplied. This type of multiplication is crucial in algebra for simplifying and solving problems that contain binomial terms.When multiplying a binomial by a scalar or another binomial, each term in the first quantity is multiplied by each term in the second. In our specific problem, we have a single scalar, \(-2\), multiplying the binomial \(x+2\). We use the distributive property as follows:

• Multiply \(-2\) by \(x\)
• Multiply \(-2\) by \(+2\)

Using these steps, the multiplication results in the expanded form: \(-2x - 4\). This highlights how each component of a binomial multiplies with other terms, resulting in a comprehensible algebraic expression.

Algebraic Expressions

Algebraic expressions are combinations of variables, numbers, and operations that represent a particular value or set of values. Understanding these expressions is foundational to advanced mathematics and everyday problem-solving.In the expression \(-2(x+2)\), we see a typical algebraic expression where variables and constants interact. The expression includes both a scalar and a binomial enclosed in parentheses, showcasing how elements within an algebraic expression can be distributed and simplified.Upon simplifying the original expression, the result \(-2x - 4\) demonstrates how algebraic expressions can be transformed and presented in a cleaner form. Recognizing different parts and their roles within expressions helps in tackling various algebra problems effectively.