If a + b = 5 and ab = 6, Find: (a3 + b3)2 - 9a2b2(a + b)2
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. -6875.
a3 + b3 = (a + b)3 – 3ab(a + b) = 53 – 3 × 6 × 5 = 125 – 90 = 35
⇒ (a3 + b3)2 = 352 = 1225
9a2b2(a + b)2 = 9 × 62 × 52 = 9 × 36 × 25 = 8100
(a3 + b3)2 - 9a2b2(a + b)2
= 1225 - 8100
= –6875