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

2 min read Jun 16, 2024
(a-b)=3 And Ab=5 Then A3-b3= Answer

Finding the Value of a³ - b³

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

Key Algebraic Identities:

We'll use the following algebraic identity to simplify our problem:

  • a³ - b³ = (a - b)(a² + ab + b²)

Step 1: Find a² + ab + b²

  • Square the equation (a - b) = 3: (a - b)² = 3² a² - 2ab + b² = 9
  • Add 3ab to both sides: a² - 2ab + b² + 3ab = 9 + 3ab a² + ab + b² = 9 + 3ab
  • Substitute the value of ab = 5: a² + ab + b² = 9 + 3(5) a² + ab + b² = 24

Step 2: Substitute Values into the Identity

Now we have the values for (a - b) and (a² + ab + b²):

  • a - b = 3
  • a² + ab + b² = 24

Substitute these values into the identity:

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

Therefore, the value of a³ - b³ is 72.

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