/*! 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 55 Find each product or quotient. ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 55

Find each product or quotient. $$ (5 k)(5 k) $$

Short Answer

Expert verified
25k^2

Step by step solution

01

Identify the Given Expression

We are given the expression \( (5k)(5k) \).
02

Apply the Multiplication Rule

When multiplying two terms, multiply the coefficients (numbers) together and then multiply the variables. Here the coefficients are both 5, so calculate \( 5 \times 5 \). For the variables, multiply \( k \times k \).
03

Simplify the Coefficients

Multiply the coefficients: \( 5 \times 5 = 25 \).
04

Simplify the Variables

Multiply the variables: \( k \times k = k^2 \).
05

Combine the Results

Combine the simplified coefficients and variables: \( 25k^2 \).

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.

Coefficients
In the given exercise, we deal with coefficients, which are the numerical parts of terms. In \( (5k)(5k) \), the coefficients are both 5.
To multiply coefficients, you simply perform regular multiplication with them. Here, the coefficients are 5 and 5. Multiply them:
\[ 5 \times 5 = 25 \]
Remember, coefficients are just numbers. Anytime you need to multiply monomials, start with the coefficients and then move on to the variables. This makes the problem easier to handle step by step.
Variables
Variables in expressions are letters that represent numbers. In \( (5k)(5k) \), the variable we're working with is k. Multiplying variables follows particular rules in algebra.
When you multiply like variables, such as \( k \times k \), you add the exponents of the variables. Since k (or k to the power of 1) multiplied by k equals \( k^{1+1} = k^2 \).
This might seem confusing at first, but remember that it's basically adding the powers of the variables being multiplied together. So \( k \times k \) equals \[ k^2 \]. Keep practicing and it'll become second nature.
Simplification
Simplification is combining all parts of an expression into its most compact and understandable form.
In our example \( (5k)(5k) \), we found that multiplying the coefficients gives us 25, and multiplying the variables gives us \[ k \times k = k^2 \].
Combining these, we get our simplified product: \[ 25k^2 \].
Simplifying expressions is key to making them easier to work with and understand. Always remember to break down the multiplication into smaller steps, simplify each part, and then combine them for your final answer.

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

Simplify each expression. $$ x-0.03(x+500) $$

Solve each problem. Nursing home costs. The average cost of a 1 -year stay in a nursing home in 2007 was \(\$ 75,190\) (www.medicare.gov). In \(n\) years from 2007 the average cost will be \(75,190(1.05)^{n}\) dollars. Find the projected cost for a 1 -year stay in 2020

Simplify. $$ \frac{-6 x y z-3 x y+9 z}{-3} $$

Simplify each expression. $$ 3(5 x+2)-2(2 x+4)+x $$

Perform these computations. $$(-3)(0.19)$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Decision 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.