/*! 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 6 Simplify each expression, if pos... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 6

Simplify each expression, if possible. $$6.3 a b^{2}+7 a^{2} b$$

Short Answer

Expert verified
The simplified expression is \(6.3 a b^{2} + 7 a^{2} b\).

Step by step solution

01

Check for common factors

The first step in simplifying an algebraic expression is to look for any common factors. For the given expression, there does not appear to be a common factor in both terms, other than 'a', which can't be factored out, because, in the second term 'a' is squared and in the first one it's not, so they're not similar terms.
02

Simplify the expression

As the two terms are not similar and no common factors can be simplified, the expression is already in its simplest form.

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.

Simplification of Algebraic Expressions
Simplifying an algebraic expression means making it as concise and straightforward as possible, without changing its value. It involves combining like terms and factoring when applicable. In the given exercise, where the expression is \(6.3ab^2 + 7a^2b\), we aim to make sure there are no unnecessary complexity or redundancies.
To simplify expressions, follow these steps:
  • Identify any common factors across terms.
  • Look for like terms that can be combined.
  • Apply any potential mathematical operations like addition, subtraction, or factoring.

In this case, since the terms \(ab^2\) and \(a^2b\) are dissimilar, the expression \(6.3ab^2 + 7a^2b\) is already simplified. No further reduction or combination can be done.
Understanding Common Factors
Common factors are numbers or variables that divide all terms in an expression without a remainder. Finding these is crucial as they allow for simplification by grouping and factoring out terms. In our example, we attempt to find common factors for \(6.3ab^2\) and \(7a^2b\).
Here are simple steps to identify common factors:
  • Look at each term separately and identify the numerical and variable parts.
  • Check if there are common numerical factors (like 2, 3, 5, etc.).
  • Check for common variable factors: common letters that appear in each term.

For \(6.3ab^2 + 7a^2b\), while both terms share the variable \(a\) and \(b\), they don't actually have the same power or enough commonality to factor them together without changing their expression form. Thus, no further simplification can occur through common factors.
Like Terms in Algebraic Expressions
Like terms in algebra are terms that have identical variable parts. This means that they can be combined through addition or subtraction. For an expression to be simplified by combining like terms, it requires the terms to have the exact same variables raised to the same powers.
In our given expression \(6.3ab^2 + 7a^2b\), inspect each term:
  • The term \(6.3ab^2\) includes \(a\) and \(b^2\).
  • The term \(7a^2b\) includes \(a^2\) and \(b\).

Since one has \(b^2\) and the other has \(a^2\), they are not like terms due to the differing exponents and cannot be merged. When simplifying, exclusively like terms (same variables to the same powers) should be combined, which is why in this scenario, it doesn't apply. Thus, each remains separate.

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

Express each solution as an inequality. Plane altitudes A pilot plans to fly at an altitude of between 17,500 and 21,700 feet. To the nearest tenth, what will be the range of altitudes in miles? (Hint: There are 5,280 feet in 1 mile.)

Consider the problem: How many gallons of a \(10 \%\) and a \(20 \%\) solution should be mixed to obtain a \(30 \%\) solution? Without solving it, how do you know that the problem has no solution?

Find the solution of \(1 < \frac{1}{x} .\) (Hint: Will any negative values of \(x\) work?)

Solve each inequality and graph the solution on the number line. $$1 \leq-7 x+8 \leq 15$$

Solve each inequality and graph the solution on the number line. $$3 \leq 2 x-1 < 5$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

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.