(x2 - y2) (a2– b2) + 4abxy
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(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 )
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