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Chapter 6: Problem 10

Add or subtract the monomials. $$4 y^{3}+6 y^{3}$$

Short Answer

Expert verified
10y^{3}

Step by step solution

01

Identify the Like Terms

Both monomials have the same variable raised to the same power, which means they are like terms. The terms are: \(4y^{3}\) and \(6y^{3}\).
02

Add the Coefficients

To combine the like terms, add their coefficients together. The coefficients are 4 and 6. So, we have: \(4 + 6 = 10\).
03

Combine the Like Terms

Attach the common variable part \(y^{3}\) to the sum of the coefficients. So, you get \(10y^{3}\).

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Key Concepts

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

like terms
When working with monomials, it's crucial to identify 'like terms'. Like terms are terms with the same variables raised to the same power. For instance, in the exercise given, we have the terms \(4y^{3}\) and \(6y^{3}\). Both terms have exactly the same variable \(y\) raised to the power of 3.
This similarity makes them like terms.

In order to combine terms, they must be like terms.
Otherwise, they cannot be added or subtracted directly.
Keep an eye for such terms in your equations and expressions to make your calculations easier.
coefficients
The coefficient in a term is the numerical factor that multiplies the variable part of the term. For example, in \(4y^{3}\), the coefficient is 4, and in \(6y^{3}\), it is 6.
To add or subtract monomials, you simply deal with their coefficients.

First, extract the coefficients from the terms: 4 and 6.
Then, add these coefficients:
\(4 + 6 = 10\).
After working with the coefficients, the next step is to reattach the variable part.
combining like terms
Once you've identified like terms and worked with the coefficients, the final step is combining them.
After adding the coefficients 4 and 6:
\(4 + 6 = 10\).

Attach the common variable part, \(y^{3}\), to the sum of the coefficients: \(10y^{3}\).
Combining like terms simplifies your expressions and equations, which makes them easier to read and work with.

This process is incredibly important in algebra as it helps in solving and simplifying equations efficiently.

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Most popular questions from this chapter

Divide each polynomial by the binomial. $$\left(x^{2}-14 x+49\right) \div(x-7)$$

Divide each polynomial by the monomial. $$\left(16 y^{2}-20 y\right) \div 4 y$$

Divide each polynomial by the binomial. $$\left(q^{2}+2 q+20\right) \div(q+6)$$

Divide each polynomial by the binomial. $$\left(2 n^{3}-10 n+24\right) \div(n+3)$$

Mixed Practice $$(4 y)\left(12 y^{7}\right) \div 8 y^{2}$$
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