Problem 2 - Elementary Algebra

Question

For the following problems, write the number of terms that appear, then write the terms. $$ 14 y^{6} $$

Step-by-Step Solution

Answer

Answer: There is 1 term in the expression and the term is \(14y^6\).

Step 1: Identify the number of terms

There is only one term in the given expression: \(14y^6\).

Step 2: Write down the term

The term present in the expression is \(14y^6\). To summarize, there is one term in the expression and the term itself is \(14y^6\).

Key Concepts

Number of Terms in an Expression

Understanding the number of terms in an algebraic expression is a foundational concept in algebra. In a given expression, terms are the parts of the expression that are separated by addition or subtraction signs. For instance, in the expression \(2x + 3y - 4z\), there are three terms: \(2x\), \(3y\), and \(4z\).

However, it’s important to note that coefficients, variables, and exponents within those terms do not create additional separation. Take our exercise: the expression given is \(14y^6\) which may look complex because of the coefficient (14) and the exponent (6), but it's actually just one term. There are neither plus nor minus signs to separate it into more terms. Understanding this will help you analyze algebraic expressions more effectively.

Identifying Terms in Algebra

Identifying terms in an algebraic expression allows you to break down and understand the structure of the expression. Terms are the building blocks, consisting of numbers, variables, and possibly exponents. When looking at an expression, like \(5x^2 + 7x - 3\), identify each term by looking for plus and minus signs that act as dividers. But it's not enough just to spot the terms; recognizing their types is crucial:

• A constant term is a number with no variable, like -3.
• A variable term includes a variable (like x) and may include a number called a coefficient (like 5 in 5x).
• A coefficient is a number that multiplies a variable within a term, such as 5 in 5x^2.

In identifying terms, you can also pinpoint their roles in equations and functions, paving the way for simplifying expressions, solving equations, and more.

Monomial Term

A monomial term is where our main exercise focuses on. It’s an algebraic expression that contains only one term. The term monomial comes from 'mono-' meaning single and '-nomial' pertaining to terms. A monomial can be a constant number, a variable, or a product of numbers and variables raised to powers.

For example, \(14y^6\) is a monomial because it only has one term, not separated by plus or minus signs, and it comprises a coefficient (14) and a variable (y) raised to a power (6). Recognizing a monomial is straightforward as it doesn't involve addition or subtraction within the expression. Monomials play a key role in algebra, especially when learning about polynomial expressions and operations like addition, subtraction, and multiplication of polynomials.