How do you factor #1/8 + 8x^3#?

1 Answer
George C.
Dec 19, 2015

Use the sum of cubes identity to find:

#1/8+8x^3 = (1/2+2x)(1/4-x+4x^2)#

Explanation:

The sum of cubes identity can be written:

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

Both #1/8 = (1/2)^3# and #8x^3 = (2x)^3# are perfect cubes, so it is natural to use the sum of cubes identity to help factor this, putting #a=1/2# and #b=2x# ...

#1/8+8x^3#

#=(1/2)^3+(2x)^3#

#=(1/2+2x)((1/2)^2-(1/2)(2x)+(2x)^2)#

#=(1/2+2x)(1/4-x+4x^2)#

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