Problem 504 Add or subtract the monomials. ... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 504

Add or subtract the monomials. $$\text { Add} \ 4 n^{5},-n^{5},-6 n^{5}$$

Short Answer

Expert verified

The result is $-3n^5$.

Step by step solution

Identify Like Terms

Notice that all the given terms are monomials with the same variable and exponent: $4n^5, -n^5, -6n^5$. Since they all contain $n^5$, they can be combined.

Combine the Coefficients

Add or subtract the coefficients of the like terms: $4 + (-1) + (-6)$. This gives: $4 - 1 - 6 = -3$.

Write the Result

Multiply the combined coefficient by the common part $n^5$: $-3n^5$. This is the simplified form.

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Key Concepts

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

like terms

When dealing with monomials, identifying like terms is super important. Like terms are terms that have the exact same variables raised to the same power.
In this exercise, we have the terms: $4n^5, -n^5, -6n^5$. All of these terms are considered like terms because they share the same variable $n$ and the same exponent (5).
This is a key step because combining non-like terms is not possible when adding or subtracting monomials. Always ensure the terms have identical variables and exponents before you proceed.

coefficients

In a monomial, the coefficient is the numerical part that multiplies the variable part. For example, in the term $4n^5$, the coefficient is 4.
In our exercise, the coefficients are 4, -1, and -6. These coefficients will be added or subtracted while retaining the common variable part $n^5$.
When combining coefficients, align them properly according to their signs: $4 + (-1) + (-6)$. This simplifies to: $4 - 1 - 6 = -3$.
Combining coefficients correctly is crucial as it directly impacts the final simplified expression.

exponents

Exponents indicate how many times a variable is multiplied by itself. In these monomials, the exponent is 5, as seen in terms like $4n^5$ and $-6n^5$.
Note that since all the terms have the same exponent, this allows them to be added or subtracted directly, only affecting the coefficients.
Remember, you do not change the exponent when adding or subtracting like terms. Therefore, after calculating the combined coefficients (-3 in this case), the variable part with its exponent remains the same, resulting in $-3n^5$.
This rule applies regardless of the number of like terms involved.

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91影视

Add or subtract the monomials. $$\text { Add} \ 4 n^{5},-n^{5},-6 n^{5}$$

Short Answer

Step by step solution

Identify Like Terms

Combine the Coefficients

Write the Result

Key Concepts

like terms

coefficients

exponents

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