How do you simplify #x^3+3# ?

1 Answer
Apr 30, 2016

Answer:

#x^3+3=(x+root(3)(3))(x^2-root(3)(3)x+root(3)(9))#

Explanation:

This is already in simplest form unless you count factorisation.

We can treat this expression as a sum of cubes and use the sum of cubes identity:

#a^3+b^3=(a+b)(a^2-ab+b^2)#

with #a=x# and #b=root(3)(3)# as follows:

#x^3+3#

#=x^3+(root(3)(3))^3#

#=(x+root(3)(3))(x^2-x(root(3)(3))+(root(3)(3))^2)#

#=(x+root(3)(3))(x^2-root(3)(3)x+root(3)(9))#