If 5x - 4y = 7 and xy = 8, find: 125x³ - 64y³

Using the formula,

[∵ (x - y)³ = x³ - y³ - 3xy(x - y)]

So,

⇒ (5x - 4y)³ = (5x)³ - (4y)³ - 3 $\times$ 5x $\times$ 4y(5x - 4y)

⇒ (5x - 4y)³ = 125x³ - 64y³ - 60xy(5x - 4y)

Putting the value (5x - 4y) = 7 and xy = 8, we get

⇒ (7)³ = 125x³ - 64y³ - 60 $\times$ 8 $\times$ 7

⇒ 343 = 125x³ - 64y³ - 3,360

⇒ 125x³ - 64y³ = 343 + 3,360

⇒ 125x³ - 64y³ = 3,703

Hence, the value of 125x³ - 64y³ is 3,703.