Question

How do you expand `(5m^3-1)^3`?

Answer 1

`25m^6 - 10m^3 + 1`

Explanation:

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

First step: expand the brackets. To expand the above question, we have to remember that when we have a power/exponent/a little number above the brackets i.e. "n" , it means we have to multiply the function/number/letter in front, "n" number of times.

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

Second step: simplify the equation by multiplying the first two brackets and leaving the third bracket, constant.

`(5m^3 - 1)(5m^3 - 1)`
`5m^3(5m^3) + 5m^3(-1) - 1(5m^3) - 1(-1)`
`25m^6 - 5m^3 - 5m^3 + 1`
`25m^6 - 10m^3 + 1`

Note: when multiplying numbers that have powers, you must add the powers but multiply the numbers.
E.g. `5m^3 * 5m^3 = 5 * 5 * m^(3 +3) = 25m^6`