Question

Factorisation of (x^2-y^2)(a^2-b^2)+4abxy

Answer 1

Heya user,

( x² - y² )( a² - b² ) + 4abxy

= (ax)² - (ay)² - (bx)² + (by)² + 4abxy
= (ax)² + (by)² + 2axby - [ (ay)² + (bx)² - 2aybx ]
= [ ax + by ]² - [ ay - bx ]²   < ----------- of form ( m² - n² )
= [ ax + by + ay - bx ] [ ax + by - ay + bx ]
= [ a(x+y) - b(x-y)] [ a(x-y) + b(x+y) ]