Question

How do you factor `125+t^3`?

Answer 1

`(5+t)(25+5t+t^2)`

As `color(blue)(a^3+b^3` can be written in the form
`color(blue)((a+b)(a^2+ab+b^2)` This is called the sum of cubes.

So, first of all write
`125+t^3` in the form `5^3+t^3`
Now, using the sum of cubes.

`5^3+t^3`= `(5+t)(5^2+5t+t^2)`
=`(5+t)(25+5t+t^2)`