(i) a² + 8a + 16

= a² + 2× a × 4 + 4²

Using identity (a + b)² = a² + 2ab + b²

Here a =a; b = 4

a² + 2× a × 4 + 4²

= (a + 4)²

^{= (a + 4)(a + 4)}

(ii) p² -10p + 25

= p² - 2× 5 × p + 5²

Using identity (a - b)² = a² - 2ab + b²

Here a =p; b = 5

p² - 2× 5 × p + 5²

= (p - 5)²

= (p-5)(p-5)

(iii) 25m² + 30m + 9

= (5m)² + 2 × 5 × 3 × m + 3²

Using identity (a + b)² = a² + 2ab + b²

Here a =5m; b = 3

(5m)² + 2 × 5 × 3 × m + 3²

= (5m + 5)²

= (5m + 5)(5m + 5)

(iv) 49y² + 84yz + 36z²

= (7y)² + 2 × 7 × 6 × y × z + (6z)²

Using identity (a + b)² = a² + 2ab + b²

Here a =7y; b = 6z

(7y)² + 2 × 7 × 6 × y × z + (6z)²

= (7y + 6z)²

= (7y + 6z)(7y + 6z)

(v) 4x² - 8x + 4

= (2x)² - 2 × 2 × 2× x + 2²

Using identity (a - b)² = a² - 2ab + b²

Here a =2x; b = 2

(2x)² - 2 × 2 × 2× x + 2² 

= (2x - 2)²

= (2x - 2)(2x - 2)

(vi) 121b² - 88bc + 16c²

= (11b)² - 2 × 11b × 4c + (4c)²

Using identity (a - b)² = a² - 2ab + b²

Here a =11b; b = 4c

(11b)² - 2 × 11b × 4c + (4c)²

= (11b – 4c)²

= (11b – 4c)(11b – 4c)

(vii) (l + m)² - 4lm 

Expand (l + m)² = l² + 2lm + m²

[using (a + b)² = a² + 2ab + b²]

l² + 2lm + m² - 4lm

⇒ l² - 2lm + m²

= l² - 2 × l × m + m²

Using identity (a - b)² = a² - 2ab + b²

Here a =l; b = m

l² - 2 × l × m + m²

= (l – m)²

= ( l - m)(l - m)

(viii) a⁴ + 2a²b² + b⁴

_{= (a}²)² + 2 × a² × b² + (b²)²

Using identity (a + b)² = a² + 2ab + b²

Here a = a²; b = b²

(a²)² + 2 × a² × b² + (b²)²

= (a² + b²)²

= (a² + b²)(a² + b²)