Problem 31 Add or subtract the monomials. ... [FREE SOLUTION]

Chapter 6: Problem 31

Add or subtract the monomials. Subtract \(5 x^{6}\) from \(-12 x^{6}\).

Short Answer

Expert verified

-17 x^{6}

Step by step solution

Identify the Operation

Recognize that you need to subtract the monomial \(5 x^{6}\) from \(-12 x^{6}\). The operation to perform is subtraction.

Set Up the Expression

Write the subtraction expression: \(-12 x^{6} - 5 x^{6}\).

Combine Like Terms

Since both terms are like terms (they contain the same variable raised to the same power), subtract the coefficients: \(-12 - 5 = -17\).

Write the Result

Combine the coefficient with the variable part to get the final result: \(-17 x^{6}\).

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 a single term algebraic expression that consists of a coefficient and a variable raised to a non-negative power.
For example, in the exercise, both \(5x^{6}\) and \(-12x^{6}\) are monomials.
They have one term each. To clarify, consider these points:

The coefficient is the numerical part (e.g., -12 in \(-12x^{6}\)).
The variable part includes the variable and its exponent (in this case, \(x^{6}\)).

Remember, monomials do not have any addition or subtraction within them. They are straightforward algebraic expressions.

Subtraction

Subtraction in algebra is similar to basic arithmetic, but it involves variables and their exponents.
In this exercise, you are asked to subtract one monomial from another. Let's break it down:

Write down the expression correctly. We're given to subtract \(5x^{6}\) from \(-12x^{6}\).
That means setting up the expression as \(-12x^{6} - 5x^{6}\).

When you subtract, you'll focus on the coefficients first, leaving the variable part untouched.
This ensures you manage the numbers and the algebraic terms correctly.

Like Terms

Like terms are terms whose variables (and their exponents) are the same. In algebra, only like terms can be combined.
For example, in the given exercise \(-12x^{6}\) and \(5x^{6}\) are like terms because they both feature \(x^{6}\).

Identify like terms by checking the variable and the exponent.
Combine them by adding or subtracting their coefficients.

Here's how it works in our exercise:
The coefficients are -12 and 5. Subtract these: \(-12 - 5 = -17\).
Finally, attach the variable part \(x^{6}\) to get \(-17x^{6}\).
This is how you simplify expressions by combining like terms.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Add or subtract the monomials. Subtract \(5 x^{6}\) from \(-12 x^{6}\).

Short Answer

Step by step solution

Identify the Operation

Set Up the Expression

Combine Like Terms

Write the Result

Key Concepts

Monomials

Subtraction

Like Terms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Pure Maths

Logic and Functions

Mechanics Maths

Probability and Statistics

Calculus

Study anywhere. Anytime. Across all devices.