Factorise :
a3 - 27a3\dfrac{27}{a^3}a327
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Given,
=a3−27a3=(a)3−(3a)3=(a−3a)[(a)2+a×3a+(3a)2]=(a−3a)(a2+3+9a2).\phantom{=} a^3 - \dfrac{27}{a^3} \\[1em] = (a)^3 - \Big(\dfrac{3}{a}\Big)^3 \\[1em] = \Big(a - \dfrac{3}{a}\Big)\Big[(a)^2 + a \times \dfrac{3}{a} + \Big(\dfrac{3}{a}\Big)^2\Big] \\[1em] = \Big(a - \dfrac{3}{a}\Big)\Big(a^2 + 3 + \dfrac{9}{a^2}\Big).=a3−a327=(a)3−(a3)3=(a−a3)[(a)2+a×a3+(a3)2]=(a−a3)(a2+3+a29).
Hence, a3−27a3=(a−3a)(a2+3+9a2).a^3 - \dfrac{27}{a^3} = \Big(a - \dfrac{3}{a}\Big)\Big(a^2 + 3 + \dfrac{9}{a^2}\Big).a3−a327=(a−a3)(a2+3+a29).
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