Respuesta :
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:
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
[tex]a^3-b^3[/tex] and [tex]a^3+b^3[/tex]
1) [tex]64+a^{12}b^{51}[/tex]
64 can written as [tex]64=4^3[/tex] and [tex]a^{12}b^{51}=(a^4b^{17})^3[/tex]
So, [tex]64+a^{12}b^{51}[/tex] can be written as [tex](4)^3+(a^4b^{17})^3[/tex]
2) [tex]-t^6+u^3v^{21}[/tex]
[tex]-t^6[/tex] can written as [tex]-t^6=(-t^2)^3[/tex] and [tex]u^3v^{21}=(uv^{7})^3[/tex]
So, [tex]-t^6+u^3v^{21}[/tex] can be written as [tex](-t^2)^3+(uv^{7})^3[/tex]
3) [tex]8h^{45}-k^{15}[/tex]
[tex]8h^{45}[/tex] can written as [tex]8h^{45}=(2\sqrt{2}h^{15})^3[/tex] and [tex]k^{15}=(k^5)^3[/tex]
So, [tex]8h^{45}-k^{15}[/tex] can be written as [tex](2\sqrt{2}h^{15})^3-(k^5)^3[/tex]
Thus, only (1) , (2) and (3) can be written as sums or differences of two cubes
