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Chapter 1: Problem 110

Identify the terms in each expression. $$ -4-3 x+2 x y $$

Short Answer

Expert verified
-4, -3x, 2xy

Step by step solution

01

- Identify Individual Components

First, recognize each separate term in the expression. The given expression is ewline $$-4-3x + 2xy$$. Separate the terms based on the addition and subtraction signs.
02

- List the Terms

Break down the expression into its terms. The first term is ewline $$-4$$, the second term is ewline $$-3x$$, and the third term is ewline $$2xy$$.
03

- Confirm the Terms

Verify that all parts of the expression are included: ewline $$-4, -3x, 2xy$$ are indeed all of the terms in the original expression.

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Key Concepts

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

Identifying Algebraic Terms
Algebraic terms are the building blocks of algebraic expressions. Each term can be a constant, a variable, or a combination of both. In the expression given, there are three distinct terms:
  • -4
  • -3x
  • 2xy
To identify terms, look for parts of the expression separated by addition (+) or subtraction (鈭�) signs. Each part between these signs is considered an individual term. For instance, in our expression -4 - 3x + 2xy:- The term -4 is a constant.- The term -3x is a variable with a coefficient.- The term 2xy involves two variables multiplied together with a coefficient.Understanding how to identify each term is crucial for simplifying and solving algebraic expressions.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can contain constants, variables, and operators. Our expression -4 - 3x + 2xy is a typical example. Here鈥檚 a quick breakdown:- A constant is a fixed value, such as -4 in our case.- Variables, represented by letters like x and y, can change or represent unknown values.- Operators, such as addition (+) and subtraction (鈭�), combine the terms in specific ways.Algebraic expressions can represent real-life problems and help solve equations. By learning to identify and manipulate these expressions, we gain the tools to handle more complex mathematical tasks.
Addition and Subtraction in Algebra
Addition and subtraction are fundamental operations in algebra. These operations combine or separate terms in an algebraic expression. Let鈥檚 see how they work with our expression -4 - 3x + 2xy:
  • When we see a negative sign in front of a term, like -4 and -3x, it means we subtract that term.
  • A plus sign, like in + 2xy, means we add that term.
Combining like terms, which have the same variables raised to the same power, can simplify expressions. In our example, there are no like terms to combine, so each term remains separate.Understanding addition and subtraction helps simplify equations and solve for variables in algebra.

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Most popular questions from this chapter

Simplify. $$ 9 t^{4}+7 t-5\left(9 t^{3}-2 t\right) $$

List in order from least to greatest. $$-\frac{2}{3}, \frac{1}{2},-\frac{3}{4},-\frac{5}{6}, \frac{3}{8}, \frac{1}{6}$$

Simplify. $$ 4 a-b-4(5 a-7 b+8 c) $$

Evaluate. $$ (-x)^{2}-5 x, \text { for } x=-3 $$

Simplify using a calculator. Round your answer to the nearest thousandth. $$ \frac{13.4-5|1.2+4.6|}{(9.3-5.4)^{2}} $$
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