Problem 12 Add or subtract the monomials. ... [FREE SOLUTION]

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Chapter 6: Problem 12

Add or subtract the monomials. $$-3 m+9 m$$

Short Answer

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Step by step solution

Identify like terms

Both terms $ -3m $ and $ 9m $ are like terms because they have the same variable $ m $ with the same exponent.

Combine the coefficients

Add the coefficients of the like terms: $ -3 + 9 $.

Perform the arithmetic

Calculate the sum of the coefficients: $-3 + 9 = 6$.

Multiply the sum by the variable

Combine the sum with the variable $ m $ to get $ 6m $.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Monomials

Monomials are the simplest type of algebraic expressions. They contain a single term made up of different parts like a coefficient and variables. For example, in the expression $9m$, $-3m$, the parts are:

A coefficient, which is a number (like -3 or 9).
A variable, which is usually a letter (like 'm').

Monomials can also include variables with exponents, like $4x^2$. A key point about monomials is that they do not contain addition or subtraction operators within the term. When combining like terms in monomials, it is essential to ensure the variables and their exponents match.

Coefficients

The coefficient is the number that appears in front of the variable in a term. In $-3m$ and $9m$, the numbers -3 and 9 are the coefficients. Coefficients tell us how many times the variable is being counted. When combining like terms, you simply add or subtract the coefficients. Here鈥檚 what you need to know about coefficients:

They are typically real numbers.
They can be positive, negative, or zero.

Combining the coefficients $-3 and 9$ in the exercise involves performing the arithmetic operation $-3 + 9$, which equals 6. That means the combined term would have a coefficient of 6.

Variables

Variables are symbols, often letters like $x$, $y$, or $m$, that represent unknown values. In our exercise, the variable is $m$. Variables can be raised to different powers, which affects how you combine the terms. Important points about variables are:

They represent unknown quantities and can change.
They must match (including their exponents) in order to combine them as like terms.

In our example, since both terms $-3m$ and $9m$ have the variable $m$ with no exponent (or an exponent of 1), they can be combined by adding their coefficients. The result is $6m$. Variables help us simplify and solve mathematical expressions and equations efficiently.

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91影视

Add or subtract the monomials. $$-3 m+9 m$$

Short Answer

Step by step solution

Identify like terms

Combine the coefficients

Perform the arithmetic

Multiply the sum by the variable

Key Concepts

Monomials

Coefficients

Variables

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