Question

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

64 + a12b51
–t6 + u3v21
8h45 – k15
75 – n3p6
–27 – xz9

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

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

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√(2)h^(15))^3` and
`k^(15)=(k^5)^3`

So,
`8h^(45)-k^(15)` can be written as
`(2√(2)h^(15))^3-(k^5)^3`

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