2021 · Q40
If 2x − 3y − 7 = 0, then what is the value of 8x³ − 36x²y + 54xy² − 27y³ − 340 ?
Elementary MathematicsAlgebra
- A−1
- B0
- C1
- D3
Explanation
The first four terms are exactly (2x − 3y)³, since (a−b)³ = a³ − 3a²b + 3ab² − b³ with a = 2x, b = 3y. Given 2x − 3y = 7, the expression is 7³ − 340 = 343 − 340 = 3. This is option (d).