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Given : a - b = - 8 and ab = - 12
To find : a³ - b³
Solution :
a - b = -8
By cubing on both the sides
[Since (x - y)³ = x³ - x³ - 3xy(x - y) = x³ - y³]
[Since given that ab = -12 and a - b = -8]
(x - y)³ = x³ - x³ - 3xy(x - y) = x³ - y³
1] (x + y)² = x² + y² + 2xy
2] (x - y)² = x² + y² - 2xy
3] (x + y)(x - y) = x² - y²
4] (x + a)(x + b) = x² + (a + b)x + ab
5] (x + y)³ = x³ + y³ + 3xy(x + y)
6] (x - y)³ = x³ + y³ - 3xy(x - y)