How do you factor completely #125x^3+1 #?

1 Answer
Mar 1, 2017

Answer:

#(5x+1)(25x^2-5x+1)#

Explanation:

#125x^3+1" is a " color(blue)"sum of cubes"# and is factorised, in general, as shown below.

#color(red)(bar(ul(|color(white)(2/2)color(black)(a^3+b^3=(a+b)(a^2-ab+b^2))color(white)(2/2)|)))#

#125x^3=(5x)^3" and "1=(1)^3#

#"here "a=5x" and "b=1#

#rArr125x^3+1=(5x+1)(25x^2-5x+1)#