Identify monomials, binomials and trinomials from the following algebraic expressions:
`ax^(2) +bx xx y^(2)`

Answer

To solve the problem of identifying monomials, binomials, and trinomials from the given algebraic expression \( ax^2 + bx \cdot y^2 \), we will follow these steps:

### Step 1: Understand the Definitions
- **Monomial**: An algebraic expression that contains only one term. For example, \( 4x \) or \( xy^2 \).
- **Binomial**: An algebraic expression that contains exactly two terms. For example, \( 4x^2 + y \) or \( xy^2 + z \).
- **Trinomial**: An algebraic expression that contains exactly three terms. For example, \( x^2 + xy + z \).

### Step 2: Analyze the Given Expression
The expression given is \( ax^2 + bx \cdot y^2 \).

### Step 3: Simplify the Expression
We can rewrite the expression to clearly see the terms:
\[ ax^2 + (bx \cdot y^2) \]
This can be interpreted as:
\[ ax^2 + bxy^2 \]

### Step 4: Count the Terms
Now, we can identify the number of terms in the expression:
1. The first term is \( ax^2 \).
2. The second term is \( bxy^2 \).

### Step 5: Identify the Type of Expression
Since there are **two terms** in the expression \( ax^2 + bxy^2 \), we classify it as a **binomial**.

### Conclusion
The expression \( ax^2 + bx \cdot y^2 \) is a **binomial** because it consists of two terms.

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