(i) 9x²+6xy+y²

9x²+6xy+y² = (3x)²+(2 × 3x × y)+y²

Using identity, x² + 2xy + y² = (x + y)²

Here, x = 3x

y = y

9x²+6xy+y² = (3x)²+(2×3x×y)+y²

= (3x+y)²

= (3x+y)(3x+y)

(ii) 4y²−4y+1

4y²−4y+1 = (2y)² – (2×2y×1)+1

Using identity, x² – 2xy + y² = (x – y)²

Here, x = 2y

y = 1

4y²−4y+1 = (2y)²–(2×2y×1)+1²

= (2y–1)²

= (2y–1)(2y–1)

(iii)  x²–y²/100

x²–y²/100 = x²–(y/10)²

Using identity, x²-y² = (x - y)(x + y)

Here, x = x

y = y/10

x²–y²/100 = x²–(y/10)²

= (x–y/10)(x+y/10)