How do you factor #125+8z^3#?

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Answer 1 · 2015-12-24T05:59:13

#(5+2z)(25-10z+4z^2)# or
# (2z+ 5)(4z^2 -10z+25)#

This is a sum of cube because

#125 = 5^3#

#8z^3 = (2z)^3#

Remember the formula for sum of cube is

#x^3 + y^3 = (x+y)(x^2 -xy+y^2)#

We can rewrite #125 + 8z^3 = 5^3 + (2z)^3#

This factor to

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

or we can rewrite the factor as

#(2z + 5) (4z^2 -10z+25)# so it can be in alphabetical order (standard form for polynomial)