How do you factor # 125x^3+64#?

1 Answer
George C.
Dec 14, 2015

Use the sum of cubes identity to find:

#125x^3+64=(5x+4)(25x^2-20x+16)#

Explanation:

Both #125x^3 = (5x)^3# and #64 = 4^3# are perfect cubes, so this is a natural case for the sum of cubes identity:

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

With #a=5x# and #b=4# we find:

#125x^3+64#

#=(5x)^3+4^3#

#= (5x+4)((5x)^2-(5x)(4)+4^2)#

#=(5x+4)(25x^2-20x+16)#

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