An algebraic expression containing three terms is called a

Options

A. monomial
B. binomial
C. trinomial
D. All of these

Answer

To solve the question "An algebraic expression containing three terms is called a," we will follow these steps:

### Step 1: Understand the Types of Algebraic Expressions
Algebraic expressions can be classified based on the number of terms they contain. The main types are:
- **Monomial**: An expression with a single term (e.g., \(4x^2\)).
- **Binomial**: An expression with two terms (e.g., \(4x^2 + 4x\)).
- **Trinomial**: An expression with three terms.

### Step 2: Identify the Definition of a Trinomial
A trinomial is defined as an algebraic expression that consists of three distinct terms. Each term can have different variables and powers. For example, \(5x^2 + 5x + 1\) is a trinomial because it has three separate terms.

### Step 3: Check for Similar Terms
In order for an expression to be classified as a trinomial, it must not contain any like terms (terms that are identical). For instance, \(4x^2 + 4y + 5x^2\) is not a trinomial because \(4x^2\) and \(5x^2\) are like terms. They can be combined to form \(9x^2 + 4y\), which is a binomial.

### Step 4: Conclusion
Based on the definitions and examples provided, we can conclude that an algebraic expression containing three terms is called a **trinomial**.

### Final Answer
An algebraic expression containing three terms is called a **trinomial**.

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