Question

Write the following cubes in expand form.

(a) ( a - 2b )³ (b) ( x - 2y/3 )³​

Answer 1

To find :

• Expanded form of given question

Important Identity :

• (a-b)³ = a³ - b³ -3a²b + 3ab²

• (a+b)³ = a³ + b³ + 3a²b + 3ab²

Solution :

(a) (a-2b)³

=> (a)³ - (2b)³ - (3)(a²)(2b) + 3(a)×(2b)²

=> a³ - 8b³ - 6a²b + 3a×4b²

=> a³ - 8b³ - 6a²b + 12ab²

(b) (x - 2y/3)³

=> (x)³ - (2y/3)³ - 3(x)²×(2y/3) + 3(x)×(2y/3)²

$\implies \: {x}^{3} - \: \dfrac{8 {y}^{3} }{27} - 3 \times {x}^{2} \times \dfrac{2y}{3} + 3x \times ( \dfrac{4 {y}^{2} }{9} ) \\ \\ \implies \: {x}^{3} - \dfrac{8 {y}^{3} }{27} - 2 {x}^{2} y + \frac{4x {y}^{2} }{3}$

ANSWER :

(a) a³ - 8b³ - 6a²b + 12ab²

(b) ${x}^{3} - \dfrac{8 {y}^{3} }{27} - 2 {x}^{2} y + \dfrac{4x {y}^{2} }{3}$