Question 336005


{{{64a^3-27b^3}}} Start with the given expression.



{{{(4a)^3-(3b)^3}}} Rewrite {{{64a^3}}} as {{{(4a)^3}}}. Rewrite {{{27b^3}}} as {{{(3b)^3}}}.



{{{(4a-3b)((4a)^2+(4a)(3b)+(3b)^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)}}}



{{{(4a-3b)(16a^2+12ab+9b^2)}}} Multiply


-----------------------------------

Answer:

So {{{64a^3-27b^3}}} factors to {{{(4a-3b)(16a^2+12ab+9b^2)}}}.


In other words, {{{64a^3-27b^3=(4a-3b)(16a^2+12ab+9b^2)}}}



So the answer is D)



If you need more help, email me at <a href="mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help">jim_thompson5910@hotmail.com</a>


Also, feel free to check out my <a href="http://www.freewebs.com/jimthompson5910/home.html">website</a>. 


Jim