Question

find a^3 + 8 b^3 if a + 2b = 10 and ab = 15

Answer 1

Given a +2b = 10 and ab = 15
Consider, a3 + 8b3 = a3 + (2b)3
                              = (a + 2b)3 − 3 × a × 2b(a + 2b)  [Since, a3 + b3 = (a + b)− 3ab(a + b)]
                              = (a + 2b)3 − 6ab(a + 2b)
                              = (10)3 − 6 × 15 × 10
                              = 1000 − 900 = 100

Answer 2

a + 2b = 10
ab = 15

(a + 2b)^2 = a^2 + (2b)^2 + 4ab
100 = a^2 + 4b^2 + 4 × 15
a^2 + 4b^2 = 100 - 60
a^2 + 4b^2 = 40

a^3 + (2b)^3 = (a + 2b)( a^2 + (2b)^2 - 2ab )
a^3 + 8b^3 = 10 × ( 40 - 30 )
a^3 + 8b^3 = 10 × 10
a^3 + 8b^3 = 100

Hope it helps you