Factor polynomial $$ 27x^{6}-48 $$
Answer
$$ 27x^{6}-48 = 3( 3x^{3}-4 )( 3x^{3}+4 ) $$
Explanation
Step 1 :
After factoring out $ 3 $ we have:
$$ 27x^{6}-48 = 3 ( 9x^{6}-16 ) $$Step 2 :
Rewrite $ 9x^{6}-16 $ as:
$$ 9x^{6}-16 = (3x^{3})^2 - (4)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 3x^{3} $ and $ II = 4 $ , we have:
$$ 9x^{6}-16 = (3x^{3})^2 - (4)^2 = ( 3x^{3}-4 ) ( 3x^{3}+4 ) $$This page was created using
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