If a + b = 8 and ab = 15, find: a³ + b³

Using the formula,

[∵ (x + y)³ = x³ + y³ + 3xy(x + y)]

So,

⇒ (a + b)³ = a³ + b³ + 3ab(a + b)

Putting the value (a + b) = 8 and ab = 15, we get

⇒ (8)³ = a³ + b³ + 3 $\times$ 15 $\times$ 8

⇒ 512 = a³ + b³ + 360

⇒ a³ + b³ = 512 - 360

⇒ a³ + b³ = 152

Hence, the value of a³ + b³ is 152.