Question

factor completely:

256a^5 - 108a^2

Answer 1

If you take out a factor of 4a^2, you'll get\[4a^2(64a^3-27)\]The last factor is the difference of two cubes, which can be factored as,\[64a^3-27=(4a)^3-3^3=(4a-3)((4a)^2+(4a)(3)+3^2)\]\[=(4a-3)(16a^2+12a+9)\]so your expression can be factored as\[4a^2(4a-3)(16a^2+12a+9)\]