The adjacent sides of a rectangle are $x^{2} - 4 x y + 7 y^{2} a n d x^{3} - 5 x y^{2}$ .Find its area.

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Solution

Reqd.area= $(x^{2} - 4 x y + 7 y^{2}) (x^{3} - 5 x y^{2}) = x^{2} (x^{3} - 5 x y^{2}) - 4 x y (x^{3} - 5 x y^{2}) + 7 y^{2} (x^{3} - 5 x y^{2}) = x^{5} - 5 x^{3} y^{2} - 4 x^{4} y + 20 x^{2} y^{3} + 7 x^{3} y^{2} - 35 x y^{4} = x^{5} + (7 - 5) x^{3} y^{2} - 4 x^{4} y + 20 x^{2} y^{3} - 35 x y^{4} = x^{5} + 2 x^{3} y^{2} - 4 x^{4} y + 20 x^{2} y^{3} - 35 x y^{4} = (x^{5} - 4 x^{4} y + 2 x^{3} y^{2} + 20 x^{2} y^{3} - 35 x y^{4}) s q . u n i t .$

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