Question
Factorise: (ax + by)2 + (ay - bx)2
Solution
(ax + by)2 + (ay - bx)2
= a2x2 + b2y2 + 2abxy + a2y2 + b2x2 - 2abxy
= a2 (x2 + y2) + b2 (x2 + y2)
= (x2 + y2) (a2 + b2).
