/*! 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 7 Find each product. $$ 5 p\le... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 7

Find each product. $$ 5 p\left(3 q^{2}\right) $$

Short Answer

Expert verified
15pq^2

Step by step solution

01

Identify the terms

First, identify the terms that need to be multiplied. Here, the terms are \(5p\) and \(3q^2\).
02

Multiply the coefficients

Multiply the numerical coefficients of the terms. The coefficients are 5 and 3. \[ 5 \times 3 = 15 \]
03

Write the product

Combine the product of the coefficients with the variables: \[ 15pq^2 \]

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.

algebraic products
In algebra, finding a product involves multiplying two or more expressions. For this exercise, we are asked to multiply the expressions 5p and 3q虏.
To do this, follow these general steps:
  • Identify the terms or expressions to be multiplied.
  • Multiply the numerical coefficients.
  • Combine the product of the coefficients with the variables.
This method can be used for any algebraic expressions. Simply break down the problem into smaller, easy-to-manage steps.
coefficients
Coefficients are the numerical parts of the terms in an algebraic expression. In the given exercise, the coefficients are 5 and 3 from the terms 5p and 3q虏, respectively.
To find the product of the given expressions, we first need to multiply these coefficients. The multiplication process for coefficients is straightforward and follows the basic rules of arithmetic:
  • Multiply the numbers directly.
  • Combine them with the variables.
So in our example, we have:
\[ 5 \times 3 = 15 \]
This result gives us the coefficient for the final product.
variables
Variables in algebra are symbols that represent unknown values and can vary. In our exercise, the variables are 'p' and 'q虏'.
When multiplying expressions, it's important to keep track of these variables and their exponents:
  • The variable 'p' in 5p remains 'p' in the final product.
  • The variable 'q虏' remains 'q虏' because there are no other 'q' terms to combine it with.

The final step is to combine the multiplied coefficient with the variables:
So, multiplying 5p by 3q虏 results in:\[ 15pq虏 \]

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

To understand how the special product \((a+b)^{2}=a^{2}+2 a b+b^{2}\) can be applied to a purely numerical problem. The number 35 can be written as \(30+5 .\) Therefore, \(35^{2}=(30+5)^{2} .\) Use the special product for squaring a binomial with \(a=30\) and \(b=5\) to write an expression for \((30+5)^{2} .\) Do not simplify at this time.

Perform each division using the "long division" process. $$ \frac{6 r^{4}-11 r^{3}-r^{2}+16 r-8}{2 r-3} $$

Multiply. $$ \frac{1}{2}(4 m-8 n) $$

Match each expression in Column I with the equivalent expression in Column II. Choices in Column II may be used once, more than once, or not at all. An Exercise \(17, x \neq 0 .\). I (a) \(x^{0}\) (b) \(-x^{0}\) (c) \(7 x^{0}\) (d) \((7 x)^{0}\) (e) \(-7 x^{0}\) (f) \((-7 x)^{0}\) II A. 0 B. 1 C. -1 D. 7 E. -7 F. \(\frac{1}{7}\)

If the distance traveled is \(\left(5 x^{3}-6 x^{2}+3 x+14\right)\) miles and the rate is \((x+1) \mathrm{mph},\) write an expression, in hours, for the time traveled.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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.