Question

Factorise:

4 – x² + 10xy – 25y²

Answer 1

Given: 4 – x² + 10xy – 25y²

4 – x² + 10xy – 25y² can be written as (2)² – (x² – 10xy + 25y²)

⇒ (2)² – {(x)² – 2 × x × 5y + (5y)²}

⇒ (2)² – (x – 5y)²

Now, applying the identity, 

a² – b² = (a + b) (a – b)

⇒ (2 – x + 5y) (2 + x – 5y)

Hence, the required is (2 – x + 5y) (2 + x – 5y).