Answer:

Sure! Let's use the identity (a + b)² = a² + 2ab + b² to evaluate the expressions:

i) (420)²:

Using the identity, we have:

(420)² = (420) × (420)

= (420) × [(400) + (20)]

= (420) × (400) + (420) × (20)

= 168,000 + 8,400

= 176,400

ii) (105)²:

Using the identity, we have:

(105)² = (105) × (105)

= (105) × [(100) + (5)]

= (105) × (100) + (105) × (5)

= 10,500 + 525

= 11,025

iii) (3005)²:

Using the identity, we have:

(3005)² = (3005) × (3005)

= (3005) × [(3000) + (5)]

= (3005) × (3000) + (3005) × (5)

= 9,015,000 + 15,025

= 9,030,025

Therefore, evaluating the expressions using the given identity, we have:

i) (420)² = 176,400

ii) (105)² = 11,025

iii) (3005)² = 9,030,025

Step-by-step explanation:

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