Question

(x^2+y^2+2xy) -4xy is​

Answer 1

(x² + y² + 2xy) - 4xy

= x² + y² + 2xy - 4xy

= x² - 2xy + y²

Further if we want to factorise it,

∵ a² - 2ab + b² = (a - b)²,

∴ x² - 2xy + y² = (x - y)² = (x - y)(x - y)

ALITER:-

We know, 4ab = (a + b)² - (a - b)²

∴ (x² + y² + 2xy) - 4xy

= (x + y)² - [(x + y)² - (x - y)²]

= (x + y)² - (x + y)² + (x - y)²

= (x - y)² or (x - y)(x - y).