Factorise the following using appropriate identities :
`(i) 9x^(2)+6xy+y^(2) " " (ii) 4y^(2)-4y+1 " " (iii) x^(2)-(y^(2))/(100)`

Explanation

Let's factorize the given polynomials step by step.

### (i) Factorize \( 9x^2 + 6xy + y^2 \)

1. **Identify the terms**: The expression is \( 9x^2 + 6xy + y^2 \).
2. **Recognize the form**: This expression resembles the perfect square trinomial \( a^2 + 2ab + b^2 \).
3. **Identify \( a \) and \( b \)**: Here, \( a = 3x \) and \( b = y \).
4. **Write in identity form**: We can rewrite the expression as:
...