Problem 65 Rewrite each expression using th... [FREE SOLUTION]

Chapter 1: Problem 65

Rewrite each expression using the distributive property. Simplify if possible. $$-8(u-4)$$

Short Answer

Expert verified

Rewriting the expression using the distributive property and simplifying, we get: $-8(u - 4) = -8u + 32$.

Step by step solution

Using the distributive property

Apply the distributive property of multiplication over addition to the expression -8(u - 4). We will multiply -8 by both terms within the parentheses. $$-8(u-4) = (-8) \times u + (-8) \times(-4)$$

Simplify

Next, we will simplify the expression by performing the multiplication operations. $$-8u + (-8)(-4) = -8u + 32$$ So, the final answer after rewriting the expression using the distributive property and simplifying is: $$-8(u - 4) = -8u + 32$$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Expressions

Simplifying expressions is a crucial skill in algebra. It involves rewriting an expression in a simpler or more concise form. This process can make solving equations much easier.

In our exercise, after applying the distributive property, we get the expression $-8u + 32$. Simplifying this involves ensuring that there are no like terms that can be combined and that all the arithmetic is complete.

Here are some key points to remember when simplifying expressions:

Combine like terms: Terms that have the same variable part can be combined. For example, $3x + 4x$ simplifies to $7x$.
Perform arithmetic operations: Ensure all basic operations such as addition and multiplication are done correctly.
Look for opportunities to factor or further simplify: Sometimes, expressions can be factored or rewritten in a simpler form.

Simplifying makes expressions easier to work with and is often a step in solving equations.

Multiplication

Multiplication is one of the core arithmetic operations you need to understand, especially when working with algebraic expressions. It involves combining quantities in a specified way and forms the basis of the distributive property.

In the exercise, multiplication is applied when distributing the $-8$ across the terms inside the parentheses $(u-4)$. Here's how that works:

Multiply $-8$ by $u$ to get $-8u$.
Multiply $-8$ by $-4$ to get $+32$. Remember that a negative times a negative is a positive.

Understanding multiplication helps break down expressions efficiently, especially in more complex algebraic manipulations. Always pay attention to signs during multiplication to avoid mistakes.

Algebraic Expressions

Algebraic expressions are combinations of variables, numbers, and operations. They can represent real-world situations and are foundational in algebra.

In our example, $-8(u-4)$ is an algebraic expression. It includes:

Variables: $u$, which can take on different values.
Constants: Numbers without variables, such as $-8$ and $-4$.
Operations: Addition, subtraction, and multiplication connect the variables and constants.

Working with algebraic expressions involves understanding how to manipulate these parts, such as applying the distributive property, to simplify or solve equations. Recognizing how each component interacts helps you translate real-world problems into mathematical solutions.

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Rewrite each expression using the distributive property. Simplify if possible. $$-8(u-4)$$

Short Answer

Step by step solution

Using the distributive property

Simplify

Key Concepts

Simplifying Expressions

Multiplication

Algebraic Expressions

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