How do you factor #8x^3-125#?

1 Answer
Serena D.
Mar 24, 2018

#(2x-5)(4x^2+10x+25)#

Explanation:

Factoring difference of cubes (#a^3-b^3#): #(a-b)(a^2+ab+b^2)#

Here, #a# is #2x# because the cube root of 8 is 2 and the cube root of #x^3# is #x#, #b# is 5 because the cube root of 125 is 5.

Plug the numbers in:

#(2x-5)((2x)^2+2x*5+5^2)#

#(2x-5)(2^2x^2+10x+25)#

#(2x-5)(4x^2+10x+25)#

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