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