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Chapter 2: Problem 84

Simplify by combining like terms whenever possible. $$4 a-2 b-5 c$$

Short Answer

Expert verified
The expression \(4a - 2b - 5c\) cannot be simplified further since there are no like terms.

Step by step solution

01

- Identify the like terms

In the expression \(4a - 2b - 5c\), identify the terms that can be combined. Here, each term is different: \(4a\) is a term in \(a\), \(2b\) is a term in \(b\), and \(5c\) is a term in \(c\).
02

- Check for like terms

Since there are no like terms (i.e., no terms with the same variable and exponent), the expression cannot be simplified further by combining terms.

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Key Concepts

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

Combining Like Terms
Combining like terms is a fundamental concept in algebra. It involves merging terms that have the exact same variables and exponents. For instance, in the expression 3x + 4x, both terms have the variable x. We can combine them to get 7x.
To combine like terms, follow these steps:
  • Identify which terms have the same variables and exponents.
  • Add or subtract the coefficients of these terms.
  • Ensure that you only combine terms with exactly the same variables and exponents.
In the given exercise, the terms are 4a, -2b, and -5c. These terms are not like terms because they have different variables: a, b, and c. As such, they can't be combined further.
Simplification
Simplification in algebra means reducing an expression to its simplest form. This typically involves combining like terms and performing any applicable arithmetic operations.
When simplifying, look for:
  • Like terms that can be combined.
  • Constants that can be added or subtracted.
  • Any common factors that can be factored out.
Consider the expression 4a - 2b - 5c. We need to check for any possible simplifications:
  • There are no like terms in this expression.
  • The terms have different variables.
  • We cannot combine them further.
Thus, the expression 4a - 2b - 5c is already simplified. Always remember: simplifying doesn't change the value of the expression, it just makes it easier to work with.
Variables and Coefficients
Understanding variables and coefficients is crucial in algebra.
  • A variable is a symbol, usually a letter, that represents an unknown number (e.g., a, b, c).
  • A coefficient is a number that multiplies the variable (e.g., in 4a, 4 is the coefficient).
The terms in an algebraic expression consist of both variables and coefficients. Let's break down the expression 4a - 2b - 5c:
  • 4 is the coefficient of the variable a.
  • -2 is the coefficient of the variable b.
  • -5 is the coefficient of the variable c.
Each of these terms is distinct because they involve different variables. Recognizing this helps in properly combining like terms and simplifying expressions.
Remember, combining coefficients is only possible when the terms involved have the same variables and exponents.

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Most popular questions from this chapter

Simplify by combining like terms whenever possible. $$-5 s^{2}+3 s t-s^{2}+6 s^{2}$$

Simplify by combining like terms whenever possible. $$3 x^{2}+7 x+x^{2}+3 x$$

Simplify each expression as completely as possible. $$-4(2 r-3 s)+6(s-r)$$

The surface area \(S\) of a closed rectangular box of length \(L\), width \(W\), and height \(H\) is \(S=2 L W+2 W H+2 L H .\) Find the surface area of a rectangular box of length 0.85 meter, width \(1.60 \mathrm{m},\) and height \(2.25 \mathrm{m} .\) Round off the answer to the nearest hundredth.

Evaluate the given expression for \(x=0.24\) and \(y=-0.5 .\) Round off to the nearest thousandth where necessary. $$\frac{5}{x y}$$
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