Question

( 2/3x -3/2y)² +2xy find the value by suitable Identity​

Answer 1

$\bf{\bigg(\dfrac{2}{3}x - \dfrac{3}{2}y\bigg)^{2} + 2xy}\\\\\\\\= \sf{\bigg(\dfrac{2x}{3}-\dfrac{3y}{2}\bigg)^{2} + 2xy}\\\\\\\\= \sf{\bigg[\bigg(\dfrac{2x}{3}\bigg)^{2} + \bigg(\dfrac{3y}{2}\bigg)^{2} - 2\bigg(\dfrac{2x}{3}\bigg) \bigg(\dfrac{3y}{2}\bigg)\bigg]+2xy}\\\\\\\\= \sf{\dfrac{4x^{2} }{9}+\dfrac{9y^{2} }{4} - 2xy + 2xy}\\\\\\\\= \sf{\dfrac{4x^{2} }{9}+\dfrac{9y^{2} }{4}}\\\\\\\\= \boxed{\large{\bf{\dfrac{16x^{2} + 81y^{2} }{36}}}}$

Identity used:

• (a - b)² = a² + b² - 2ab

Know more:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$