Question : What is the value of $64 x^3+38 x^2 y+20 x y^2+y^3$, when $x=3$ and $y=-4$?
Option 1: 1236
Option 2: 488
Option 3: 536
Option 4: 1256
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Correct Answer: 1256
Solution :
Substituting $x=3$ and $y=-4$ into the expression.
$64 x^3+38 x^2 y+20 x y^2+y^3$
$= 64(3)^3 + 38(3)^2(-4) + 20(3)(-4)^2 + (-4)^3$
$= 64(27) - 38(36) + 20(3)(16) - 64$
$= 1728 - 1368 + 960 - 64 = 1256$.
Hence, the correct answer is 1256.
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