(3a 1/a)^3 = (3a^2 1/a)^3 ⇒(3a^2)^3 3× (3a^2)^2(1)+3× (3a^2)1^2 1^2/a^3 ⇒27a^6 27a^4+9a^2 1/a^3 ⇒ #160; 27a^3 27a + 9/a 1/a^3 ...

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Division of a Polynomial by a Monomial

3a - 1/a3

Question

${(3 a - \frac{1}{a})}^{3}$

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Solution

$(3 a - \frac{1}{a})^{3} = (\frac{3 a^{2} - 1}{a})^{3}$
$\Rightarrow \frac{(3 a^{2})^{3} - 3 \times (3 a^{2})^{2} (1) + 3 \times (3 a^{2}) 1^{2} - 1^{2}}{a^{3}}$
$\Rightarrow \frac{27 a^{6} - 27 a^{4} + 9 a^{2} - 1}{a^{3}}$
$\Rightarrow 27 a^{3} - 27 a + \frac{9}{a} - \frac{1}{a^{3}}$

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