How do you factor #125-216r^3#?

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Answer 1 · 2017-07-02T14:36:39

#(5-6r)(25 +30r +36r^2)#

This type of expression is known as the difference of two cubes.
Each term is a perfect cube.

It has a standard way of being factorised.
#(a^3 - b^3) = (a-b)(a^2 +ab +b^2)#

In the same way:

#125 -216r^3 = (5-6r)(25 +30r +36r^2)#

Answer 2 · 2017-07-02T17:13:37

#(5-6r)(25+30r+36r^2)#

#125-216r^3#

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

#5^3-3^3*2^3*r^3#

#(5-3*2*r)(5^2+5*3*2r+(3*2*r)^2)#

#(5-6r)(25+30r+36r^2)#