How do you factor #x^3 -8#?

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Answer 1 · 2014-10-29T01:09:55

#x^3 - 8# is the difference of two cubes and can be factored in the following pattern.

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

#a^3# factors to a
#b^3# factors to b

The pattern of the signs follows the acronym SOAP
S = same sign as the cubes
O = opposite sins of the cubes
AP = always positive

#x^3# factors to x
#8# factors to 2

#x^3 - 8 = (x - 2)(x^2 + 4x + 4)#

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