Factorise :
(623)2−(213)2\Big(6\dfrac{2}{3}\Big)^2 - \Big(2\dfrac{1}{3}\Big)^2(632)2−(231)2
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= (203)2−(73)2\Big(\dfrac{20}{3}\Big)^2 - \Big(\dfrac{7}{3}\Big)^2(320)2−(37)2
Using the formula
[∵ (x2 - y2) = (x + y)(x - y)]
=(203+73)(203−73)=((20+7)3)((20−7)3)=(273)(133)=(27×133×3)=(3519)=39= \Big(\dfrac{20}{3} + \dfrac{7}{3}\Big)\Big(\dfrac{20}{3} - \dfrac{7}{3}\Big)\\[1em] = \Big(\dfrac{(20 + 7)}{3}\Big)\Big(\dfrac{(20 - 7)}{3}\Big)\\[1em] = \Big(\dfrac{27}{3}\Big)\Big(\dfrac{13}{3}\Big)\\[1em] = \Big(\dfrac{27 \times 13}{3 \times 3}\Big)\\[1em] = \Big(\dfrac{351}{9}\Big)\\[1em] = 39=(320+37)(320−37)=(3(20+7))(3(20−7))=(327)(313)=(3×327×13)=(9351)=39
Hence,(623)2−(213)2\Big(6\dfrac{2}{3}\Big)^2 - \Big(2\dfrac{1}{3}\Big)^2(632)2−(231)2 = 39
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