Identify monomials, binomials and trinomials from the following algebraic expressions :
`a^(2)-b^(2)-c^(2)+5abc`

Answer

To identify whether the given algebraic expression \( a^2 - b^2 - c^2 + 5abc \) is a monomial, binomial, trinomial, or another type of polynomial, we will follow these steps:

### Step 1: Understand the Definitions
- **Monomial**: An expression with only one term.
- **Binomial**: An expression with exactly two terms.
- **Trinomial**: An expression with exactly three terms.
- **Polynomial**: An expression with more than three terms.

### Step 2: Identify the Terms in the Expression
The given expression is:
\[ a^2 - b^2 - c^2 + 5abc \]

We will break it down into its individual terms:
1. \( a^2 \)
2. \( -b^2 \)
3. \( -c^2 \)
4. \( +5abc \)

### Step 3: Count the Number of Terms
Now, we count the number of distinct terms:
- \( a^2 \)
- \( -b^2 \)
- \( -c^2 \)
- \( +5abc \)

There are a total of **four terms** in the expression.

### Step 4: Classify the Expression
Since there are four terms in the expression, it does not fit into the categories of monomial, binomial, or trinomial. Instead, it is classified as a **quadrinomial** (an expression with four terms).

### Final Answer
The expression \( a^2 - b^2 - c^2 + 5abc \) is a **quadrinomial**.

---