If x = 3y + 4, then what is the value of (x3 - 27y3 - 36 xy)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 64.
x = 3y + 4
⇒ x - 3y = 4 ..(1
a3 - b3 = a3 - b3 - 3ab(a - b)
Applying cube on both sides in eq(1 -
⇒ (x - 3y)3 = 43
⇒ x3 - (3y)3 - 3 × x × 3y(x - 3y) = 64
⇒ x3 - 27y3 - 3 × x × 3y(4) = 64
⇒ x3 - 27y3 - 36xy = 64