Option A:
Difference of cubes
Solution:
Given expression is [tex]27 x^{3}-64[/tex].
27 can be written as [tex]3^3[/tex].
64 can be written as [tex]4^3[/tex].
[tex]27 x^{3}-64=3^3x^3-4^3[/tex]
[tex]27 x^{3}-64=(3x)^3-4^3[/tex]
To find the identity to rewrite the given expression:
Option A: Difference of cubes
[tex]27 x^{3}-64[/tex] can be rewritten as [tex](3x)^3-4^3[/tex].
That means the difference of two cubes.
So, it is true.
Option B: Difference of squares
[tex]27 x^{3}-64[/tex] cannot be written as square terms.
So, it is false.
Option C: Sum of cubes
[tex]27 x^{3}-64[/tex] cannot be written as sum of cubes.
So, it is false.
Option D: Pythagorean Triples
[tex]27 x^{3}-64[/tex] cannot be written as Pythagorean Triples.
So, it is false.
Hence difference of cubes if the correct answer.
