Question

(a2-b2)(x2-y2)+4abxy​

Answer 1

(x² - y²)(a²-b²) + 4abxy

= x²( a² - b²) - y²( a² - b²) + 4abxy

= a²x² - b²x² - a²y² + b²y² + 4abxy

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

= [ (ax)²+ (by)² + 2ax × by] - [(bx)² + (ay)² - 2bx×ay]

= ( ax + by )² - ( bx - ay )²

= [ (ax+by)+(bx-ay)][ (ax+by) - (bx-ay)]

= ( ax + by +bx - ay )(ax + by - bx + ay )

= ( ax + bx + by - ay )( ax - bx + by + ay )