Question

Factorise the following:

1 + x²y² + 4xy – x² – y²

Answer 1

Given: 1 + x²y² + 4xy – x² – y²

⇒ 1 + x²y² + 2xy – (–2xy) – x² – y²

⇒ [1² + 2xy + (xy)²] – [x² – 2xy + y²]

⇒ (xy + 1)² – (x + y)²

We know that,

(a + b) (a – b) = a² – b²

Hence,

⇒ (xy + 1 + x + y) (xy + 1 – x – y)