Question 182026

{{{54-16y^3}}} Start with the given expression



{{{2(27-8y^3)}}} Factor out the GCF {{{2}}}



Now let's focus on the inner expression {{{27-8y^3}}}



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{{{27-8y^3}}} Start with the given expression.



{{{(3)^3-(2y)^3}}} Rewrite {{{27}}} as {{{(3)^3}}}. Rewrite {{{8y^3}}} as {{{(2y)^3}}}.



{{{(3-2y)((3)^2+(3)(2y)+(2y)^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)}}}



{{{(3-2y)(9+6y+4y^2)}}} Multiply



So {{{27-8y^3}}} factors to {{{(3-2y)(9+6y+4y^2)}}}.



In other words, {{{27-8y^3=(3-2y)(9+6y+4y^2)}}}



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So {{{2(27-8y^3)}}} factors further to {{{2(3-2y)(9+6y+4y^2)}}}




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Answer:

So {{{54-16y^3}}} completely factors to {{{2(3-2y)(9+6y+4y^2)}}}