Respuesta :
You can open those brackets and distribute one brackets content with multiplication to other bracket contents.
The products which result in a sum or difference of cubes is given by:
Option D: [tex](x+4)(x^2 -4x + 16)[/tex]
What is sum or difference of cubes?
If there are two terms which are with power 3 (ie cubed), and they both are in addition or subtraction, then that is called sum or difference of cubes for two terms.
Example: [tex]a^3 - b^3[/tex] is difference of cubes.
There is a formula too which you can use in case if you need it which goes like this:
[tex]a^3 + b^3 = (a+b)(a^2 - ab + b^2)\\ \\ a^3 - b^3 = (a-b)(a^2 + ab + b^2)[/tex]
Checking all options whether they result in a sum or difference of cubes
Option A: [tex](x-4)(x^2 + 4x - 16)[/tex]
[tex](x-4)(x^2 + 4x - 16) = x^3 + 64 -4x^2 + 4x^2 -16x - 16x = x^3 +4^3 -32x[/tex]
Thus, not a sum or difference of cubes
Option B: [tex](x-1)(x^2 - x+ 1)[/tex]
[tex](x-1)(x^2 - x+ 1) = x^3 - 1 + x + x -x^2 - x^2 = x^3 - 1 + 2x - 2x^2[/tex]
Thus, not a sum or difference of cubes
Option C: [tex](x + 1) (x - 1)[/tex]
[tex](x + 1) (x - 1) = x^2 - 1 + x - x = x^2 - 1[/tex]
It is difference of squares but not of cubes.
Option D: [tex](x+4)(x^2 -4x + 16)[/tex]
[tex](x+4)(x^2 -4x + 16) = x^3 + 64 -4x^2 + 16x + 4x^2 - 16x = x^3 + 64 = x^3 + 4^3\\ (x+4)(x^2 -4x + 16) = x^3 + 4^3[/tex]
Thus, it is sum of cubes.
Thus, only Option D: [tex](x+4)(x^2 -4x + 16)[/tex] is expressible as sum or product of cubes (here it is expressible as sum of cubes [tex]x^3[/tex] and [tex]4^3[/tex].
Learn more about sum or difference of cubes here:
https://brainly.com/question/16044387
