Question

(5x/y+y/5x)³.
I want to expand this expression​

Answer 1

$Expansion \: of \: \Big( \frac{5x}{y} +\frac{y}{5x}\Big)^{3}$

$= \Big(\frac{5x}{y}\Big)^{3} + 3\times \Big(\frac{5x}{y}\Big)^{2} \times \Big(\frac{y}{5x}\Big)+ 3 \times \Big(\frac{5x}{y}\Big)\times \Big(\frac{y}{5x}\Big)^{2} + \Big(\frac{y}{5x}\Big)^{3}$

/* By Algebraic Identity */

$\boxed{\pink{ (a+b)^{3} = a^{3}+3a^{2}b+3ab^{2}+b^{3} }}$

$= \frac{125x^{3}}{y^{3}} + 3\times \frac{5x}{y} + 3 \times \frac{y}{5x} + \frac{y^{3}}{125x^{3}}$

$= \frac{125x^{3}}{y^{3}} + \frac{15x}{y} + \frac{3y}{5x} + \frac{y^{3}}{125x^{3}}$

Therefore.,

$\red{Expansion \: of \: \Big( \frac{5x}{y} +\frac{y}{5x}\Big)^{3}}$

$\green{= \frac{125x^{3}}{y^{3}} + \frac{15x}{y} + \frac{3y}{5x} + \frac{y^{3}}{125x^{3}}}$

•••♪

Answer 2

Step-by-step explanation:

125x³/y³ + 15x/y + 3y/5x + y³/125x³.