/*! 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 62 Multiply. See Example 4 $$(2 t... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 62

Multiply. See Example 4 $$(2 t+5)(-2)$$

Short Answer

Expert verified
The expression \((2t + 5)(-2)\) simplifies to \(-4t - 10\).

Step by step solution

01

Distribute the First Term

Start with the expression \((2t + 5)(-2)\). Distribute the term \(-2\) to each term inside the parentheses. First, multiply \(-2\) by \(2t\):\[-2 imes 2t = -4t\].
02

Distribute the Second Term

Next, multiply \(-2\) by the constant term \(5\) inside the parentheses:\[-2 imes 5 = -10\].
03

Combine the Results

Combine the results of the two products to form the final expression. The expression \((2t + 5)(-2)\) simplifies to:\[-4t - 10\].

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.

Understanding Algebraic Expressions
An algebraic expression is a mathematical phrase that can contain numbers, variables, and operators. In our exercise, the expression is \(2t + 5\), which includes:
  • \(2t\), where \(2\) is a coefficient and \(t\) is a variable.
  • A constant term, \(5\).
These expressions are fundamental in algebra and provide a way to represent real-world problems using symbols. They help in carrying out operations, such as addition, subtraction, and multiplication. Understanding algebraic expressions is the first step to manipulating them effectively.
Mastering Multiplication of Terms
Multiplying terms within an expression is all about applying the distributive property. This property allows you to multiply a single term by each term inside a set of parentheses. In our example, the term \(-2\) is multiplied by each term in \(2t + 5\). Here鈥檚 how it works:
  • First, multiply \(-2\) by \(2t\), which gives \(-4t\).
  • Then, multiply \(-2\) by \(5\), resulting in \(-10\).
This step-by-step multiplication ensures every term is accounted for, allowing accurate simplification of the expression. Mastering this multiplication process is essential for solving more complex algebraic problems.
Introduction to Polynomials
A polynomial is an algebraic expression that can have multiple terms, including constants, variables, and exponents. The given expression \(2t + 5\) is a binomial, a type of polynomial with exactly two terms. Polynomials can range from simple, like in our example, to more complex with several variables and higher powers. Knowing how to work with polynomials is crucial because:
  • They can model a wide range of real-world problems.
  • They form the basis for advanced mathematical concepts.
By understanding polynomials, their structure, and how they interact through operations like multiplication, you can tackle a variety of algebraic challenges more effectively.

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

An __________ is a mathematical sentence that contains an \(=\) symbol.

Fill in the blanks. The set of _____ numbers is \(\\{0,1,2,3,4,5, \ldots\\},\) the set of _____ numbers is \(\\{1,2,3,4,5, \ldots\\},\) and the set of ______ is \(\\{. . .,-2,-1,0,1,2, \ldots\\}\)

Complete each property of addition. Then give its name. a. \(a+(-a)=\square\) b. \(a+0=\square\) c. \(a+b=b+\square\) d. \((a+b)+c=a+\square\)

Simplify by combining like terms. See Example 5 . $$-9 a+11 a d-35 a+a d$$

Find the volume of each figure to the nearest hundredth. See Example 4. (Answers may vary slightly depending on which approximation of is used.) A pyramid whose base is a square with each side measuring \(2.57 \mathrm{cm}\) and with a height of \(12.32 \mathrm{cm}\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.