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D e a r s t u d e n t, I a s s u m e t h a t y o u r q u e s t i o n t o f a c t o r i s e t h e g i v e n e x p r e s s i o n i) (a^{2} - b^{2}) (c^{2} - d^{2}) - 4 a b c d = a^{2} c^{2} - a^{2} d^{2} - b^{2} c^{2} + b^{2} d^{2} - 4 a b c d = a^{2} c^{2} + b^{2} d^{2} - 2 a b c d - a^{2} d^{2} - b^{2} c^{2} - 2 a b c d U \sin g x^{2} + y^{2} - 2 x y = {(x - y)}^{2} a n d x^{2} + y^{2} + 2 x y = {(x + y)}^{2} = {(a c - b d)}^{2} - (a^{2} d^{2} + b^{2} c^{2} + 2 a b c d) = {(a c - b d)}^{2} - {(b c + a d)}^{2} U \sin g x^{2} - y^{2} = (x + y) (x - y) = (a c - b d + b c + a d) (a c - b d - b c - a d) = (a (c + d) + b (c - d)) (a (c - d) - b (a + d)) i i) 4 x^{2} - y^{2} - 3 x y + 2 x - 2 y = x^{2} + 3 x^{2} - y^{2} - 3 x y + 2 x - 2 y = (x^{2} - y^{2}) + (3 x^{2} - 3 x y) + (2 x - 2 y) x^{2} - y^{2} = (x + y) (x - y) = (x + y) (x - y) + 3 x (x - y) + 2 (x - y) = (x - y) (x + y + 3 x + 2) = (x - y) (4 x + y + 2) R e g a r d s

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