Question

factorise (x^2-y^2)(a^2-b^2)+4abxy

Answer 1

$(x^{2} - {y}^{2} )( {a}^{2} - {b}^{2} ) + 4abxy \\ = {a}^{2} {x}^{2} + {b}^{2} {y}^{2} - {a }^{2} {y}^{2} - {x}^{2} {b}^{2} + 2abxy + 2abxy \\ = ( {a}^{2} {x}^{2} + 2abxy + {b}^{2} {y}^{2} ) - ( {a}^{2} {y}^{2} - 2abxy + {x}^{2} {b}^{2} ) \\ = (ax + by)^{2} - {(ay - bx)}^{2} \\ = (ax + by + ay - bx)(ax + by - ay + bx).....ans$
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