If a + b = 25, then (a – 15)3 + (b – 10)3 is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 0
Given:
a + b = 25
Formula:
(x - y)3 = x3 - y3 - 3xy(x - y)
Calculations:
⇒ a + b = 25
⇒ (a - 15) = (10 - b)
According to the question;
⇒ (a - 15)3 + (b - 10)3
⇒ 100 - b3 - 30b × (10 - b) + b3 - 1000 - 30b × (b - 10) = 0
Hence, the required value is 0.