Question

if a-b=3 and ab=4 find a3-b3

Answer 1

(a-b)3= (a-b)(a2+b2+ab)
=(a-b)(a2+b2+ab+2ab-2ab)
=(a-b)((a2+b2-2ab)+3ab)
=(a-b)((a-b)2+3ab)
now put values
3 (9+12)
=63

Answer 2

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

Answer: 63