(a-b)=3 And Ab=5 Then A3-b3=

Jasonbradley

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Jun 16, 2024

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Finding the Value of a³ - b³

Given that (a - b) = 3 and ab = 5, we can find the value of a³ - b³.

Using the Difference of Cubes Formula

The difference of cubes formula states:

a³ - b³ = (a - b)(a² + ab + b²)

We already know (a - b) = 3. Let's find (a² + ab + b²) using the information provided:

1. Square the equation (a - b) = 3: (a - b)² = 3² a² - 2ab + b² = 9

2. Add 3ab to both sides: a² - 2ab + b² + 3ab = 9 + 3ab a² + ab + b² = 9 + 3ab

3. Substitute ab = 5: a² + ab + b² = 9 + 3(5) a² + ab + b² = 24

Now we can plug the values into the difference of cubes formula:

a³ - b³ = (a - b)(a² + ab + b²) a³ - b³ = (3)(24) a³ - b³ = 72

Therefore, the value of a³ - b³ is 72.