Question

What identity can be used to rewrite the expression 27x^3-64?

Answer 1

Option A:

Difference of cubes

Solution:

Given expression is $27 x^{3}-64$.

27 can be written as $3^3$.

64 can be written as $4^3$.

$27 x^{3}-64=3^3x^3-4^3$

$27 x^{3}-64=(3x)^3-4^3$

To find the identity to rewrite the given expression:

Option A: Difference of cubes

$27 x^{3}-64$ can be rewritten as $(3x)^3-4^3$.

That means the difference of two cubes.

So, it is true.

Option B: Difference of squares

$27 x^{3}-64$ cannot be written as square terms.

So, it is false.

Option C: Sum of cubes

$27 x^{3}-64$ cannot be written as sum of cubes.

So, it is false.

Option D: Pythagorean Triples

$27 x^{3}-64$ cannot be written as Pythagorean Triples.

So, it is false.

Hence difference of cubes if the correct answer.