Question

(X/2+y/3)^3 - (x/2-y/3)^3

Answer 1

Step-by-step explanation:

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

$given \\ a = \frac{x}{2} + \frac{y}{2} \: and \: \: b \: = \frac{x}{2} - \frac{y}{2}$

By substituting the values of a and b in the formula mentioned above, we get

$( a- b) = \frac{x}{2} + \frac{y}{2} - ( \frac{x}{2} - \frac{y}{2} ) \: \\ = \frac{x}{2} - \frac{x}{2} + \frac{y}{2} + \frac{y}{2} \\ = \frac{2y}{2} \\ = y$

Similarly we can find the value of other part and multiply the products and you'll get your answer