How do you factor #8m³ - 27n³#?

1 Answer
Jan 23, 2016

Answer:

#(2m-3n)(4m^2+6mn+9n^2)#

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# can be expressed as #(2m)^3-(3n)^3#, we can factor this as if #a=2m# and #b=3n#.

#8m^3-27n^3#

#=(2m)^3-(3n)^3#

#=(2m-3n)((2m)^2+2m(3n)+(3n)^2)#

#=(2m-3n)(4m^2+6mn+9n^2)#