How do you factor #8m³ - 27n³#?
1 Answer
Jan 23, 2016
Explanation:
Both of these terms are cubed term:
#8m^3=(2m)^3# #27n^3=(3n)^3#
Because of this, this expression is a difference of cubes.
This is a fairly common pattern that can be factored as
#a^3-b^3=(a-b)(a^2+ab+b^2)#
Since
#8m^3-27n^3#
#=(2m)^3-(3n)^3#
#=(2m-3n)((2m)^2+2m(3n)+(3n)^2)#
#=(2m-3n)(4m^2+6mn+9n^2)#