Question

factorise : (ac + by)² + (bx - ay)²

Answer 1

(ax + by)² + (bx - ay)²

= a²x² + b²y² + 2abxy + b²x² + a²y² - 2abxy

= a²x² + b²y² + b²x² + a²y²

= a²x² + a²y² + b²x² + b²y² 

= a² (x² + y²) + b²(x² + y²)

= (x² + y²)(a² + b²)