Simplify:
(2−3−2−4)(2−3+2−4)(2^{-3} - 2^{-4})(2^{-3} + 2^{-4})(2−3−2−4)(2−3+2−4)
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(2−3−2−4)(2−3+2−4)=(123−124)(123+124)=(18−116)(18+116)(2^{-3} - 2^{-4})(2^{-3} + 2^{-4})\\[1em] = \Big(\dfrac{1}{2}^3 - \dfrac{1}{2}^4\Big)\Big(\dfrac{1}{2}^3 + \dfrac{1}{2}^4\Big)\\[1em] = \Big(\dfrac{1}{8} - \dfrac{1}{16}\Big)\Big(\dfrac{1}{8} + \dfrac{1}{16}\Big)(2−3−2−4)(2−3+2−4)=(213−214)(213+214)=(81−161)(81+161)
LCM of 8 and 16 is 2 x 2 x 2 x 2 = 16
=(1×28×2−1×116×1)(1×28×2+1×116×1)=(216−116)(216+116)=(2−116)(2+116)=(116)(316)=(3256)= \Big(\dfrac{1 \times 2}{8 \times 2} - \dfrac{1 \times 1}{16 \times 1}\Big)\Big(\dfrac{1 \times 2}{8 \times 2} + \dfrac{1 \times 1}{16 \times 1}\Big)\\[1em] = \Big(\dfrac{2}{16} - \dfrac{1}{16}\Big)\Big(\dfrac{2}{16} + \dfrac{1}{16}\Big)\\[1em] = \Big(\dfrac{2-1}{16}\Big)\Big(\dfrac{2+1}{16}\Big)\\[1em] = \Big(\dfrac{1}{16}\Big)\Big(\dfrac{3}{16}\Big)\\[1em] = \Big(\dfrac{3}{256}\Big)=(8×21×2−16×11×1)(8×21×2+16×11×1)=(162−161)(162+161)=(162−1)(162+1)=(161)(163)=(2563)
(2−3−2−4)(2−3+2−4)=(3256)(2^{-3} - 2^{-4})(2^{-3} + 2^{-4}) = \Big(\dfrac{3}{256}\Big)(2−3−2−4)(2−3+2−4)=(2563)
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