/*! 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 9 Determine whether each is a mono... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 9

Determine whether each is a monomial, a binomial, or a trinomial. $$a^{2} b^{2}+10 a b-6$$

Short Answer

Expert verified
The given expression \(a^{2}b^{2} + 10ab - 6\) consists of 3 terms, so it is a trinomial.

Step by step solution

01

Identify the number of terms in the given expression

The given expression is: \[ a^{2}b^{2} + 10ab - 6 \] The terms are separated by "+" and "-" signs, so we can identify 3 terms in the expression, which are: 1. \(a^{2}b^{2}\) 2. \(10ab\) 3. \(-6\)
02

Determine if the expression is a monomial, binomial, or trinomial

Because the expression consists of 3 terms, it is a trinomial.

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.

Monomials
A monomial is an algebraic expression that consists of only one term. When we talk about terms, we refer to the objects in an expression separated by addition or subtraction signs.
For example, in a monomial like \(3x^2\), there are no additions or subtractions involving multiple terms. It's just a single term that includes variables, exponents, and coefficients.
  • The general structure of a monomial is \(ax^n\), where \(a\) is the coefficient, \(x\) is the variable, and \(n\) is the exponent.
  • Monomials can also be constants, like number 7, since it is one term without a variable.
Understanding monomials is a foundational skill in algebra, important not only for understanding simple expressions but also for grasping more complex polynomial expressions.
Binomials
A binomial is a polynomial that has exactly two terms. The prefix "bi-" means two, which makes it easy to remember. These terms are often chained together with a plus or minus sign.
A basic structure of a binomial looks like \(ax^m + bx^n\), where \(a\) and \(b\) are coefficients, and \(m\) and \(n\) are non-negative integers representing the exponents.
  • Binomials are considered a step up in complexity from monomials because they involve operations between two terms.
  • An example of a binomial is \(3x^2 + 5\).
Grasping how to handle binomials is crucial for solving equations, factoring, and performing algebraic manipulations.
Trinomials
Trinomials are polynomials made up of three terms. The prefix "tri-" nods to the number three, just like a triangle has three sides.
Consider the expression \(a^2b^2 + 10ab - 6\) as mentioned in our exercise. It contains three individual terms: \(a^2b^2\), \(10ab\), and \(-6\).
  • Trinomials often have a more complex structure and can be written as \(ax^2 + bx + c\), typical for quadratic equations, where \(a\), \(b\), and \(c\) are coefficients.
  • These expressions provide more room for interaction between variables and often require more involved methods for solving, such as factoring or using the quadratic formula.
Understanding trinomials is a gateway to higher-level algebra and calculus, as it often involves exploring solutions to quadratic equations and engaging in mathematical modeling.

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

Does \((y-3)^{3}=y^{3}-27 ?\) Why or why not?

If \(f(x)=\frac{1}{3} x+5,\) find \(x\) so that \(f(x)=7\)

Divide. $$\left(12 a^{4}-19 a^{3}+22 a^{2}-9 a-20\right) \div(3 a-4)$$

Divide. $$\frac{6 t^{2}-43 t-20}{t-8}$$

Multiply. $$12 k\left(\frac{1}{4} k^{2}-\frac{2}{3}\right)\left(k^{2}+1\right)$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Geometry

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.