How do you factor #40v^3-625#?

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Answer 1 · 2015-06-02T17:08:16

#40=5*8#
and #625=5*125#
So #40v^3-625=5*(8v^3)+5*(-125)#
#40v^3-625=5(8v^3-125)#

Answer 2 · 2015-06-02T20:39:59

#40v^3-625#

#=5(8v^3-125)#

#=5((2v)^3-5^3)#

#=5((2v)-5)((2v)^2+(2v)5+5^2)#

#=5(2v-5)(4v^2+10v+25)#

...using the difference of cubes identity:

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