If 3x - 4y = 5 and xy = 3, find: 27x³ - 64y³

Using the formula,

[∵ (x - y)³ = x³ - y³ - 3xy(x - y)]

So,

⇒ (3x - 4y)³ = (3x)³ - (4y)³ - 3 $\times$ 3x $\times$ 4y(3x - 4y)

⇒ (3x - 4y)³ = 27x³ - 64y³ - 36xy(3x - 4y)

Putting the value (3x - 4y) = 5 and xy = 3, we get

⇒ (5)³ = 27x³ - 64y³ - 36 $\times$ 3 $\times$ 5

⇒ 125 = 27x³ - 64y³ - 540

⇒ 27x³ - 64y³ = 125 + 540

⇒ 27x³ - 64y³ = 665

Hence, the value of 27x³ - 64y³ is 665.