Identify monomials, binomials and trinomials from the following algebraic expressions :
`x^(2)-2y^(2)`

Answer

To identify whether the given algebraic expression \( x^2 - 2y^2 \) is a monomial, binomial, or trinomial, we can follow these steps:

### Step 1: Understand the definitions
- **Monomial**: An expression with only one term. Example: \( 3x \) or \( 5y^2 \).
- **Binomial**: An expression with two terms. Example: \( x + 2 \) or \( 3a - 4b \).
- **Trinomial**: An expression with three terms. Example: \( x^2 + 3x + 2 \).

### Step 2: Identify the terms in the expression
The given expression is \( x^2 - 2y^2 \). We need to identify how many terms it has.

### Step 3: Count the terms
In the expression \( x^2 - 2y^2 \):
- The first term is \( x^2 \).
- The second term is \( -2y^2 \).

### Step 4: Determine the type of expression
Since there are two terms in the expression \( x^2 - 2y^2 \), we classify it as a binomial.

### Conclusion
The expression \( x^2 - 2y^2 \) is a **binomial** because it consists of two terms.

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