Factories the following expression-

a² + 10a + 25

In the given expression

1^st and last terms are perfect square

⇒ a² = a × a

⇒ 25 = 5 × 5

And the middle expression is in form of 2ab

10a = 2 × 5 × a

∴ a × a + 2 × 5 × a + 5 × 5

Gives (a + b)² = a² + 2ab + b²

⇒ In a² + 10a + 25

a = a and b = 5;

∴ a² + 10a + 25 = (a + 5)²

Hence the factors of a² + 10a + 25 are (a + 5) and (a + 5)