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If a + b = 8 and a + a2b +...

This question belongs to Arithmetic Ability Algebra
Algebra
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If a + b = 8 and a + a2b + b + ab2 = 128 then the positive value of a3 + b3 is:

Answer & Solution
Correct Answer: Option D
a + b = 8
a + a2b + b + ab2 = 128
(a + b) + ab(a + b) = 128
(1 + ab)(a + b) = 128
1 + ab = 16
ab = 15
a3 + b3
= (a + b)3 - 3ab(a + b)
= 512 - 3 × 15 × 8
= 512 - 360
= 152
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