Problem 62 Multiply. See Example 4 $$(2 t... [FREE SOLUTION]

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Intermediate Algebra

Alan S. Tussy, R. David Gustafson

$Math Studyset 91影视 Explanations$ Math

5 Edition

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

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 $2t$:\[-2 imes 2t = -4t\].

Distribute the Second Term

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

Combine the Results

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

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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.

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91影视

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

Short Answer

Step by step solution

Distribute the First Term

Distribute the Second Term

Combine the Results

Key Concepts

Understanding Algebraic Expressions

Mastering Multiplication of Terms

Introduction to Polynomials

One App. One Place for Learning.

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