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Chapter 6: Problem 14

Add or subtract the monomials. $$-y-5 y$$

Short Answer

Expert verified
-6y

Step by step solution

01

Identify like terms

Begin by recognizing that ewliney ewline is the variable in both monomials. Since both terms involve the same variable raised to the same power (which is ewliney^1ewline), they are like terms.
02

Combine coefficients

Now, add or subtract the coefficients of the like terms. Here, it is subtraction:ewlineyewlineCombine the coefficients: ewline-1 - 5.ewlineThis gives us ewline-6.ewlineSo we have ewline-6y.
03

Write the final expression

The result from combining the coefficients and keeping the variable part is ewline-6y.

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Key Concepts

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

Monomials
In algebra, a monomial is a single term consisting of a constant (number), a variable (such as y), or a product of constants and variables. For example, -y and -5y are both monomials.
It is important to recognize monomials because combining them follows specific rules. In our example, we have -y and -5y. Both are monomials because each is a product of a number and a variable term.
Working with monomials is the first step in understanding more complex algebraic expressions. If you master combining monomials, you will find it easier to tackle polynomials and other algebraic structures.
Coefficients
A coefficient is the numerical part of a term that contains both a number and a variable. For example, in the terms -y and -5y from our problem, the coefficients are -1 and -5 respectively.
Knowing how to identify and manipulate coefficients is crucial in algebra. When combining like terms, you will primarily focus on adding or subtracting these numbers.
In this exercise, we subtracted the coefficient of the second term (-5) from the coefficient of the first term (-1); therefore, we calculated -1 - 5 to get -6.
Always keep the variable part attached after combining coefficients, as this keeps our final expression accurate.
Variable Terms
Variable terms are parts of an algebraic expression that include a variable which can change its value. In our exercise, the variable term is y. Both original terms (-y and -5y) share the same variable term 'y'.
When combining like terms, it is essential that the variable part, including its exponent, matches. Here, both -y and -5y have the variable y raised to the same power, which is 1.
Since the variable parts are the same, we only needed to combine the coefficients. This resulted in the expression -6y, which still has y in it.
Always ensure that you are working with like variable terms, as mixing terms with different variables or exponents will lead to incorrect results.

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Most popular questions from this chapter

Simplify. (a) \(\frac{1}{c^{-5}}\) (b) \(\frac{1}{5^{-2}}\)

Divide each polynomial by the monomial. $$\frac{72 r^{5} s^{2}+132 r^{4} s^{3}-96 r^{3} s^{5}}{12 r^{2} s^{2}}$$

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Divide each polynomial by the monomial. $$\left(9 n^{4}+6 n^{3}\right) \div 3 n$$

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