Question

Choose the expressions that are sums or differences of two cubes.

Answer 1

It is the top three, you know this because they factor easily into cubes, so the answer is the top three, i did this on my assignment and it was correct, Purple math explains it

Answer 2

Answer:

only (1) , (2) and (3) can be written as sums or differences of two cubes

Step-by-step explanation:

Given : Some expressions.

We have to choose the expressions that are sums or differences of two cubes.

The sums or differences of two cubes is written as

$a^3-b^3$ and $a^3+b^3$

1)  $64+a^{12}b^{51}$

64 can written as $64=4^3$ and $a^{12}b^{51}=(a^4b^{17})^3$

So,  $64+a^{12}b^{51}$ can be written as $(4)^3+(a^4b^{17})^3$

2) $-t^6+u^3v^{21}$

$-t^6$ can written as $-t^6=(-t^2)^3$  and $u^3v^{21}=(uv^{7})^3$

So, $-t^6+u^3v^{21}$ can be written as $(-t^2)^3+(uv^{7})^3$

3) $8h^{45}-k^{15}$

$8h^{45}$ can written as $8h^{45}=(2\sqrt{2}h^{15})^3$ and  $k^{15}=(k^5)^3$

So, $8h^{45}-k^{15}$ can be written as $(2\sqrt{2}h^{15})^3-(k^5)^3$

 

Thus, only (1) , (2) and (3) can be written as sums or differences of two cubes