How do you factor 125+t^3?

1 Answer
Apr 10, 2015

(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)