Question

(ax+by)sq+(bx-ay)sq factorise

Answer 1

Question :-

• Factorise :- (ax + by)² + (bx - ay)²

Answer:-

Given:-

• (ax + by)² + (bx - ay)²

To find :-

• Factorise

Identity used :-

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²

Solution:-

Consider, (ax + by)² + (bx - ay)²

⇛ a²x² + b²y² + 2axby + b²x² + a²y² - 2aybx

⇛ a²x² + b²y² + b²x² + a²y²

⇛ (a²x² + a²y²) + (b²y² + b²x²)

⇛ a²(x² + y²) + b²(x² + y²)

⇛ (x² + y²)(a² + b²)

Hence, (ax + by)² + (bx - ay)² = (x² + y²)(a² + b²)