Question

20 points

Write as a power of a binomial.

`125m^(2) -15m^2+(3)/(5) m-(1)/(125)`

Answer 1

`(5m - (1)/(5))^(3)`

Explanation:

We have to write the following expression as a power of a binomial.

The expression is
`125m^(3) - 15m^(2) + (3)/(5)m - (1)/(125)`.

Now, we have to rearrange the given expression.

`125m^(3) - 15m^(2) + (3)/(5)m - (1)/(125)`

=
`(5m)^(3) - 3(5m)^(2)((1)/(5)) + 3(5m)((1)/(5))^(2) - ((1)/(5))^(3)`

=
`(5m - (1)/(5))^(3)` (Answer)

Since we know the identity as (a - b)³ = a³ - 3a²b + 3ab² - b³.