If 3x + 2y = 9 and xy = 3, find: 27x³ + 8y³

Using the formula,

[∵ (x + y)³ = x³ + y³ + 3xy(x + y)]

So,

⇒ (3x + 2y)³ = (3x)³ + (2y)³ + 3 $\times$ 3x $\times$ 2y(3x + 2y)

⇒ (3x + 2y)³ = 27x³ + 8y³ + 18xy(3x + 2y)

Putting the value (3x + 2y) = 9 and xy = 3, we get

⇒ (9)³ = 27x³ + 8y³ + 18 $\times$ 3 $\times$ 9

⇒ 729 = 27x³ + 8y³ + 486

⇒ 27x³ + 8y³ = 729 - 486

⇒ 27x³ + 8y³ = 243

Hence, the value of 27x³ + 8y³ is 243.