How do you factor #8- 27w ^ { 3}#?

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Answer 1 · 2016-12-17T02:15:03

#(2-3w)(4+6w+9w^2)#

The difference of two cubes (#a^3# and #b^3#) is given by:

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

In this example:

#a=2# [since #8=2^3#]

and

#b=3w# [since #27w^3 = (3w)^3#]

Replacing for #a# and #b# above:

#8-27w^3 = (2-3w)(2^2+2*3w+(3w)^2)#

#= (2-3w)(4+6w+9w^2)#