Problem 503 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 503

Add or subtract the monomials. $$-8 y^{3}-5 y^{3}$$

Short Answer

Expert verified

-13y^3

Step by step solution

Identify the Monomials

The given expression is egative 8y^3minus5y^3The monomials are egative 8 y^{3}andnegative5 y^{3}.

Combine the Coefficients

To add or subtract monomials, combine the coefficients while keeping the variable and its exponent the same.The coefficients are negative 8andnegative5.

Perform the Addition

Add the coefficients egative 8andnegative 5to get-13. Therefore,egative 8 y^{3}-5 y^{3}=-13 y^{3}

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Key Concepts

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

Combining Like Terms

To combine like terms, you need to focus on the parts of the terms that are similar. In algebra, 'like terms' are terms that have the same variables and powers. For example, in the expression $-8y^{3}-5y^{3}$, both terms are like terms because they each contain $y^{3}$. This similarity allows us to combine them by adding or subtracting their coefficients.

When performing operations on monomials, always check:

Variable: Ensure each term has the same variable.
Exponent: Ensure each term has the same power.

Once you confirm that the terms are like terms, you only need to combine their coefficients.

Algebraic Expressions

Algebraic expressions are combinations of numbers, variables, and operations. They can include terms like:

Constants (e.g., 3, -5)
Variables (e.g., x, y)
Coefficients (e.g., the 8 in 8y)

Here we deal specifically with monomials. A monomial is an algebraic expression with only one term. Examples include $7x$ and $-3y^{2}$. Expressions can be as simple or as complex as needed.
In the example from the exercise, $-8y^{3}-5y^{3}$, both terms are combined into one term with the same power of y. This simplifies the expression.

Coefficients

The coefficient is the numerical part of a term: the number in front of the variable. For instance, in the term $4x^{2}$, 4 is the coefficient. When combining like terms, you add or subtract the coefficients, while keeping the variable and its exponent unchanged.

In our example, \-8 and -5 are the coefficients. To combine them, simply add or subtract the numbers:

$-8 + -5 = -13$

So, the combined coefficient is -13. Therefore, $-8y^{3}-5y^{3}=-13y^{3}$. Understanding coefficients makes it easier to handle various algebraic operations.

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91影视

Add or subtract the monomials. $$-8 y^{3}-5 y^{3}$$

Short Answer

Step by step solution

Identify the Monomials

Combine the Coefficients

Perform the Addition

Key Concepts

Combining Like Terms

Algebraic Expressions

Coefficients

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