Question

Expand ${(2y-\frac{3}{y})}^3$.

• A. $8y^3-36y+\frac{54}{y}-\frac{27}{y^3}$
• B. $8y^3+36y+\frac{54}{y}-\frac{27}{y^3}$
• C. $8y^3-36y-\frac{54}{y}-\frac{27}{y^3}$
• D. None of these

Answer 1

The correct option is A $8y^3-36y+\frac{54}{y}-\frac{27}{y^3}$

We know, $(a-b{)}^3=a^3-b^3-3ab(a-b)$

$⟹$ $(a-b{)}^3=a^3-b^3-3a^{2}b+3a{b}^2$.

Then,

${(2y-\frac{3}{y})}^3$

$=(2y{)}^3-{\left(\frac{3}{y}\right)}^3$$-3(2y{)}^2\left(\frac{3}{y}\right)+3\left(2y\right){\left(\frac{3}{y}\right)}^2$

$=8y^3-\frac{27}{y^3}$$-3\left(4y^2\right)\left(\frac{3}{y}\right)+3\left(2y\right)\frac{9}{y^2}$

$=8y^3-36y+\frac{54}{y}-\frac{27}{y^3}$.

Therefore, option $A$ is correct.