Answer:
63
Step-by-step explanation:
Expand the formula (a - b)²:
(a - b)² = a² - 2ab + b²
Rearrange it to make a² + b² the subject:
a² + b² = (a - b)² + 2ab
Expand a³ - b³:
a³ – b³ = (a – b)(a² + b² + ab )
sub a² + b² = (a - b)² + 2ab:
a³ – b³ = (a – b)((a - b)² + 2ab + ab )
a³ – b³ = (a – b)((a - b)² + 3ab)
Sub a - b = 3 and ab = 4:
a³ – b³ = (3)((3)² + 3(4))
a³ – b³ = (3)(9 + 12)
a³ – b³ = (3)(21)
a³ – b³ = 63
