Using properties of determinants, prove that | x+y x x 5x+4y 4x 2x = x3. 10x + 8y 8x 3x

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soumon Let the given determinant be ( Delta ) Then, ( =x^{2} cdotleft|begin{array}{ll}3 x+2 y & 2 7 x+5 y & 5end{array}right| quadleft[text { taking } x text { common from } C_{2}right] ) [ =x^{2} cdot[5(3 x+2 y)-2(7 x+5 y)]=left(x^{2} cdot xright)=x^{3} ] Hence, ( Delta=x^{3} )

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