Find the value of a³ - b³, when a - b = 7 and ab = 6?
- 456
- 469
- 449
- None of these
Explanation
Given:
a - b = 7
ab = 6
The formula for a³ - b³ is:
a³ - b³ = (a - b)(a² + ab + b²)
= (a - b)((a - b)² + 3ab)
Substitute the values:
a³ - b³ = 7((7)² + 3(6))
= 7(49 + 18)
= 7 × 67
= 469
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