How do you factor #8x³ + 125y³#?

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Answer 1 · 2018-05-12T06:40:00

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

#8x^3 + 125y^3# is #(2x)^3+(5y)^3#

the sum of two cubes formula
#a^3 + b^3 = (a+b)(a^2-ab+b^2)#

so

#(2x)^3+(5y)^3#

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

now you can factor the second parentheses pair
#(2x+5y)color(red)((4x^2-10xy+25y^2))#

#color(red)((4x^2-10xy+25y^2) = (2x-5y)^2)#

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