How do you factor (r+6)^3-216?
1 Answer
May 2, 2016
Explanation:
The difference of cubes identity can be written:
a^3-b^3=(a-b)(a^2+ab+b^2)
We can use this with
(r+6)^3-216
=(r+6)^3-6^3
=((r+6)-6)((r+6)^2+(r+6)(6)+6^2)
=r((r^2+12r+36)+(6r+36)+36)
=r(r^2+18r+108)
Footnote
The remaining quadratic factor cannot be factorised further using Real coefficients.
It can be factorised by completing the square using Complex coefficients:
r^2+18r+108
=(r+9)^2-81+108
=(r+9)^2+27
=(r+9)^2-(3sqrt(3)i)^2
=((r+9)-3sqrt(3)i)((r+9)+3sqrt(3)i)
=(r+9-3sqrt(3)i)(r+9+3sqrt(3)i)