Separate monomial, binomial and trinomial from the following :
`(i) 2x-3 " " (ii) 3x^(2) " " (iii) 5x^(2)-8x+1 " " (iv) (2x+3)^(2) " "(v)-5x+1 " "(vi)6`

Answer

To separate monomial, binomial, and trinomial from the given expressions, we need to understand the definitions:

1. **Monomial**: An expression that contains only one term.
2. **Binomial**: An expression that contains exactly two terms.
3. **Trinomial**: An expression that contains exactly three terms.

Now, let's analyze each expression step by step:

### Step 1: Analyze the expressions

1. **Expression (i):** \(2x - 3\)
- This has two terms: \(2x\) and \(-3\).
- **Conclusion:** This is a **binomial**.

2. **Expression (ii):** \(3x^2\)
- This has only one term: \(3x^2\).
- **Conclusion:** This is a **monomial**.

3. **Expression (iii):** \(5x^2 - 8x + 1\)
- This has three terms: \(5x^2\), \(-8x\), and \(1\).
- **Conclusion:** This is a **trinomial**.

4. **Expression (iv):** \((2x + 3)^2\)
- Using the expansion formula \( (a + b)^2 = a^2 + 2ab + b^2 \):
- Here, \(a = 2x\) and \(b = 3\).
- Expanding gives \( (2x)^2 + 2(2x)(3) + (3)^2 = 4x^2 + 12x + 9\).
- This has three terms: \(4x^2\), \(12x\), and \(9\).
- **Conclusion:** This is a **trinomial**.

5. **Expression (v):** \(-5x + 1\)
- This has two terms: \(-5x\) and \(1\).
- **Conclusion:** This is a **binomial**.

6. **Expression (vi):** \(6\)
- This has only one term: \(6\).
- **Conclusion:** This is a **monomial**.

### Summary of Results:
- **Monomials:** (ii) \(3x^2\), (vi) \(6\)
- **Binomials:** (i) \(2x - 3\), (v) \(-5x + 1\)
- **Trinomials:** (iii) \(5x^2 - 8x + 1\), (iv) \((2x + 3)^2\) (after expansion)