Factories the following expression-

(x + y)² – 4xy

(Hint: first expand (x + y)²

If (a + b)² = a² + 2ab + b²

Then (x + y)² – 4xy

= x² + 2xy + y²-4xy

= x² + y²-2xy

In given expression

1^st and last terms are perfect square

⇒ x² = x × x

⇒ y² = y × y

And the middle expression is in form of 2ab

2xy = 2 × x × y

∴ x × x - 2 × y × x + y × y

Gives (a-b)² = a²-2ab + b²

⇒ In x² – 2xy + y²

a = x and b = y;

∴ x² – 2xy + y² = (x-y)²

Hence the factors of (x + y)² – 4xy are (x-y)and (x-y)