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: ![(x+4)(x^2 -4x + 16)](https://tex.z-dn.net/?f=%28x%2B4%29%28x%5E2%20-4x%20%2B%2016%29)
<h3>What is sum or difference of cubes?</h3>
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:
is difference of cubes.
There is a formula too which you can use in case if you need it which goes like this:
![a^3 + b^3 = (a+b)(a^2 - ab + b^2)\\ \\ a^3 - b^3 = (a-b)(a^2 + ab + b^2)](https://tex.z-dn.net/?f=a%5E3%20%2B%20b%5E3%20%3D%20%28a%2Bb%29%28a%5E2%20-%20ab%20%2B%20b%5E2%29%5C%5C%0A%5C%5C%0Aa%5E3%20-%20b%5E3%20%3D%20%28a-b%29%28a%5E2%20%2B%20ab%20%2B%20b%5E2%29)
<h3>Checking all options whether they result in a sum or difference of cubes</h3>
Option A: ![(x-4)(x^2 + 4x - 16)](https://tex.z-dn.net/?f=%28x-4%29%28x%5E2%20%2B%204x%20-%2016%29)
![(x-4)(x^2 + 4x - 16) = x^3 + 64 -4x^2 + 4x^2 -16x - 16x = x^3 +4^3 -32x](https://tex.z-dn.net/?f=%28x-4%29%28x%5E2%20%2B%204x%20-%2016%29%20%3D%20x%5E3%20%2B%2064%20-4x%5E2%20%2B%204x%5E2%20-16x%20-%2016x%20%3D%20x%5E3%20%2B4%5E3%20-32x)
Thus, not a sum or difference of cubes
Option B: ![(x-1)(x^2 - x+ 1)](https://tex.z-dn.net/?f=%28x-1%29%28x%5E2%20-%20x%2B%201%29)
![(x-1)(x^2 - x+ 1) = x^3 - 1 + x + x -x^2 - x^2 = x^3 - 1 + 2x - 2x^2](https://tex.z-dn.net/?f=%28x-1%29%28x%5E2%20-%20x%2B%201%29%20%3D%20x%5E3%20-%201%20%20%2B%20x%20%2B%20x%20-x%5E2%20-%20x%5E2%20%3D%20x%5E3%20-%20%201%20%2B%202x%20-%202x%5E2)
Thus, not a sum or difference of cubes
Option C: ![(x + 1) (x - 1)](https://tex.z-dn.net/?f=%28x%20%2B%201%29%20%28x%20-%201%29)
![(x + 1) (x - 1) = x^2 - 1 + x - x = x^2 - 1](https://tex.z-dn.net/?f=%28x%20%2B%201%29%20%28x%20-%201%29%20%3D%20x%5E2%20-%201%20%2B%20x%20-%20x%20%3D%20x%5E2%20-%201)
It is difference of squares but not of cubes.
Option D: ![(x+4)(x^2 -4x + 16)](https://tex.z-dn.net/?f=%28x%2B4%29%28x%5E2%20-4x%20%2B%2016%29)
![(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](https://tex.z-dn.net/?f=%28x%2B4%29%28x%5E2%20-4x%20%2B%2016%29%20%3D%20x%5E3%20%2B%2064%20-4x%5E2%20%2B%2016x%20%2B%204x%5E2%20-%2016x%20%3D%20x%5E3%20%2B%2064%20%3D%20x%5E3%20%2B%204%5E3%5C%5C%0A%28x%2B4%29%28x%5E2%20-4x%20%2B%2016%29%20%3D%20x%5E3%20%2B%204%5E3)
Thus, it is sum of cubes.
Thus, only Option D:
is expressible as sum or product of cubes (here it is expressible as sum of cubes
and
.
Learn more about sum or difference of cubes here:
brainly.com/question/16044387