Factories the following expression-

25m² – 40mn + 16n²

In the given expression

1^st and last terms are perfect square

⇒ 25m² = 5m × 5m

⇒ 16n² = 4n × 4n

And the middle expression is in form of 2ab

40mn = 2 × 5m × 4n

∴ 5m × 5m - 2 × 4n × 5m + 4n × 4n

Gives (a-b)² = a²-2ab + b²

⇒ In 25m² – 40mn + 16n²

a = 5m and b = 4n;

∴ 25m² – 40mn + 16n² = (5m-4n)²

Hence the factors of 25m² – 40mn + 16n² are (5m-4n)and (5m-4n)