Question

Factorize (ax + by) ^ 2 + (bx - ay) ^ 2​

Answer 1

Given: (ax + by)² + (bx - ay)²

To Find: factories

Solution:

$\rightarrow$ (ax + by)² + (bx - ay)²

$\rightarrow$ (ax)² + (by)² + 2(ax) (by) + (bx)² + (ay)² + (ay)² -2(bx) (ay)

$\rightarrow$ a²x² + b²y² + 2abxy + b²x² + a²y² -2abxy

$\rightarrow$ x² (a² +b²) + y²(a² +b²)

$\rightarrow$(a² + b²) (x² + y²)

$\therefore$ (a² + b²) (x² + y²) are the factors of (ax + by)² + (bx - ay)²