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Chapter 6: Problem 30

Add or subtract the monomials. Add: \(4 \mathrm{x}, 3 y,-3 x\)

Short Answer

Expert verified
The result is \(x + 3y\).

Step by step solution

01

Identify Like Terms

In the given expression, identify the terms that have the same variables and powers. The terms are: \(4x\), \(3y\), and \(-3x\). \(4x\) and \(-3x\) are like terms, while \(3y\) is not.
02

Combine Like Terms

Add or subtract the coefficients of the like terms. For \(4x\) and \(-3x\), combine the coefficients: \[4 + (-3) = 1\]Thus, \(4x + (-3x) = x\).
03

Write the Final Expression

Combine the result of the like terms with the remaining terms. The final expression is the sum of \(x\) and \(3y\), which can be written as \[x + 3y\].

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Key Concepts

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

like terms
When adding or subtracting monomials, the first thing you need to do is identify the like terms. Like terms are those terms in an expression that have the same variables raised to the same powers.
For example, in the expression: \( 4x, 3y, -3x \), both \( 4x \) and \( -3x \) are like terms because they both have the variable \( x \) with the same power (which is 1).
However, \( 3y \) is not a like term with either \( 4x \) or \( -3x \), as it has a different variable, \( y \). Identifying like terms is essential because you can only combine terms that have the same variables and powers.
Remember:
  • Like terms: Same variables and same powers
  • Unlike terms: Different variables or different powers
combine coefficients
Once you have identified the like terms, the next step is to combine the coefficients. The coefficient is the numerical part of a term.
In our expression, we identified \( 4x \) and \( -3x \) as like terms. Combine their coefficients by adding or subtracting them.
For \( 4x \, \text{and} \, -3x \):
  • Take the coefficients 4 and -3
  • Combine them: \( 4 + (-3) = 1 \)
Therefore, \( 4x \) and \( -3x \) combine to give us \( 1x \), which is simply written as \( x \).
Note that you do not change the variable part when combining coefficients. The variable \( x \) remains the same.
final expression
After combining the like terms, your last step is to write the final expression.
Let's revisit our expression:
We combined \( 4x \) and \( -3x \) to get \( x \).
Do not forget the unlike term \( 3y \) that we had left untouched.
So, the final expression is
  • The combined like terms: \( x \)
  • The remaining term: \( 3y \)
Therefore, the final expression is
\[ x + 3y \].
This is our result after adding and subtracting monomials while following the rules for like terms and combining coefficients.

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Most popular questions from this chapter

Divide each polynomial by the monomial. $$\left(63 a^{2} b^{3}+72 a b^{4}\right) \div(9 a b)$$

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

Divide each polynomial by the monomial. $$\left(8 x^{3}+6 x^{2}\right) \div 2 x$$

Divide the monomials. $$\frac{\left(6 a^{4} b^{3}\right)\left(4 a b^{5}\right)}{\left(12 a^{2} b\right)\left(a^{3} b\right)}$$

Divide each polynomial by the binomial. $$\left(a^{2}-2 a-35\right) \div(a+5)$$
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