Find the value of a^3 - b^3, when a - b = 4 and ab = 5?

Find the value of a^3 - b^3, when a - b = 4 and ab = 5?

Explanation

Given:

a - b = 4

ab = 5

The formula for a³ - b³ is:

a³ - b³ = (a - b)(a² + ab + b²)

We can also use the identity:

a³ - b³ = (a - b)³ + 3ab(a - b)

Substituting the given values:

a³ - b³ = (4)³ + 3 * 5 * 4

= 64 + 60

= 124