Answer:
The answer to your question is given below.
Explanation:
To which of the above expression is a sum or difference of cube, or not a sum or difference of cube, we shall do the following simplification:
Note: The Cube root of a particular number is simply a multiplication of an identical number in three places.
64x³ – 216
64 has a cube root of 4 and 216 has a cube root of 6. Therefore, the above expression can be written as:
4³x³ – 6³
(4x)³ – 6³
64x³ – 216 = (4x)³ – 6³
Therefore, 64x³ – 216 can be expressed as a difference of cube.
8x^9 + 27
8 has a cube root of 2, x^9 has a cube root of x³ and 27 has a
cube root of 3. Therefore, the above expression can be written as:
2³(x³)³ + 3³
(2x³)³ + 3³
8x^9 + 27 = (2x³)³ + 3³
8x^9 + 27 can be expreessed as a sum of cube
x³ + 125
125 has a cube root of 5. Therefore, the above expression can be written as:
x³ + 5³
x³ + 125 = x³ + 5³
x³ + 125 can be expressed as a sum of cube
36x³ + 121
36 and 121 has no cube root. Therefore, the above expression is not a sum or difference of cube.
x^6 – 16
x^6 has a cube root of x² and 16 has no cube root. Therefore, the above expression is not a sum or difference of cube.
Summary:
Sum or Difference of cubes
64x³ – 216
8x^9 + 27
x³ + 125
Not a Sum or Difference of cubes
36x³ + 121
x^6 – 16