/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 56 Rewrite each expression using th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 56

Rewrite each expression using the distributive property. Simplify if possible. $$(-10+3) 5$$

Short Answer

Expert verified
The simplified expression after using the distributive property and simplifying is \(-35\).

Step by step solution

01

Apply distributive property

According to distributive property, we apply multiplication on both terms inside the parentheses: $$(-10 + 3) 5 = -10 \cdot 5 + 3 \cdot 5$$
02

Perform multiplication

Now, calculate the multiplication in the expression: $$-10 \cdot 5 + 3 \cdot 5 = -50 + 15$$
03

Simplify the expression

Finally, add the results to simplify the expression: $$-50 + 15 = -35$$ So, the simplified expression is \(-35\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Simplify Expressions
When we're tasked with simplifying expressions, we're generally looking to reduce the expression to its simplest form. This often involves combining like terms or performing operations to remove parentheses. In the provided exercise, we simplify by using the distributive property, which helps us to break down more complex expressions. Here are the steps involved:
  • Initial Expansion: Begin by expanding any terms using the distributive property, as was done with \[(-10 + 3) 5\]. This is where you multiply each term inside the parentheses by the factor outside.
  • Perform Operations: Once expanded, carry out any necessary multiplicative operations. Calculate each multiplication separately, as shown with \(-10 \cdot 5\) and \(3 \cdot 5\).
  • Combine and Simplify: Finally, combine the results of the operations to reach an expression where no further mathematical operation can simplify it. The expression \(-50 + 15\) was simplified to \(-35\).
This methodical approach not only simplifies the current problem but builds a strong foundation for tackling more complex algebraic expressions.
Algebraic Expressions
Algebraic expressions are essentially mathematical phrases that can include numbers, variables, and operators. It's essential to recognize each part to simplify these expressions effectively. In our example, \((-10 + 3) 5\), while no variables are present, we treat it like any other algebraic expression, focusing on combining the numbers with multiplication.**Key Components:**
  • Numbers and Constants: Just like the numbers -10, 3, and 5, these don't change. They're the constants in the expression.
  • Operators: Addition, multiplication, subtraction鈥攊n algebraic expressions, operators determine how the numbers and variables should interact.
Understanding how these pieces fit together is crucial. By viewing the expression as a collection of these components, you can manipulate and redesign it more quickly. As you practice, recognizing and working with these components will help simplify even the most complex expressions.
Basic Algebra Concepts
Before diving deep into algebra, it's essential to grasp some basic concepts. These fundamentals serve as building blocks for understanding broader algebraic principles, such as the distributive property used in the provided example.**Core Ideas:**
  • Distributive Property: A fundamental property in algebra, it says that \(a(b + c) = ab + ac\). It's often used to break down expressions for easier computation, as seen when \((-10 + 3)\) was expanded to \(-10 \cdot 5 + 3 \cdot 5\).
  • Order of Operations: Known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), it guides the sequence of operations. This ensures expressions are simplified and solved correctly.
  • Combining Like Terms: This involves combining terms that have the same variables and powers to streamline the expression further.
Understanding these concepts ensures that the steps taken in algebra aren't just memorized but comprehended, paving the way for tackling more intricate problems with confidence.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write a mathematical expression for each and simplify. The quotient of 63 and \(-9\) increased by 7

Use the order of operations to simplify. $$\left(-\frac{3}{4}\right)(8)-2[7-(-3)(-6)]$$

Rewrite each expression using the distributive property. Simplify if possible. $$4(11-3)$$

Decide if each statement is true or false. $$-6>3$$

Write a mathematical expression for each and simplify. 9 more than the product of \(-7\) and \(-5\)
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.