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

1 Answer
Jim G.
Mar 1, 2017

(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)

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