Question 577374
I'm assuming you want to factor this




{{{1-125a^3}}} Start with the given expression.



{{{(1)^3-(5a)^3}}} Rewrite {{{1}}} as {{{(1)^3}}}. Rewrite {{{125a^3}}} as {{{(5a)^3}}}.



{{{(1-5a)((1)^2+(1)(5a)+(5a)^2)}}} Now factor by using the difference of cubes formula. Remember the <a href="http://www.purplemath.com/modules/specfact2.htm">difference of cubes formula</a> is {{{A^3-B^3=(A-B)(A^2+AB+B^2)}}}



{{{(1-5a)(1+5a+25a^2)}}} Multiply


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Answer:

So {{{1-125a^3}}} factors to {{{(1-5a)(1+5a+25a^2)}}}.


In other words, {{{1-125a^3=(1-5a)(1+5a+25a^2)}}}