Question

(1/2x +2y) whole cube​

Answer 1

$\sf\large\green{\underline { }}( { \frac{1}{2} + 2y)}^{3}$

$\sf\large\green{\underline { identity.......}} \\ \\ \sf\large\red { ( {x + y)}^{3} } = \sf\large\red { {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} + {y}^{3} }$

$\sf\large\green{\underline { }} {( \frac{1}{2x} + 2y) }^{3} \\ \\ = > \sf\green{\underline { }} { (\frac{1}{2x}) }^{3} + 3( { \frac{1}{2x} )}^{2} (2y) + 3( \frac{1}{2x} ) {(2y)}^{2} + {(2y)}^{3} \\ \\ = > \sf\large\green{\underline { }} \frac{1}{8 {x}^{3} } + 3( \frac{1}{4 {x}^{2} } )(2y) + 3( \frac{1}{2x} )(4 {y}^{2} ) + 8 {y}^{3} \\ \\ = > \sf\large\green{\underline { }} \frac{1}{8 {x}^{3} } + \frac{3y}{2 {x}^{2} } + \frac{6 {y}^{2} }{x} + 8 {y}^{3}$

Answer 2

(1/2x + 2y)³

Identity to be used:

(a + b)³ = a³ + b³ + 3ab(a + b)

→ 1/8x³ + 8y³ + 3(1/2x)(2y)(1/2x + 2y)

→ 1/8x³ + 8y³ + (3 + 12xy)/2x