Question
Factor polynomial $$ z^{4}-1296 $$
Answer
$$ z^{4}-1296 = ( z-6 )( z+6 )( z^{2}+36 ) $$
Explanation
Step 1 :
Rewrite $ z^{4}-1296 $ as:
$$ z^{4}-1296 = (z^{2})^2 - (36)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = z^{2} $ and $ II = 36 $ , we have:
$$ z^{4}-1296 = (z^{2})^2 - (36)^2 = ( z^{2}-36 ) ( z^{2}+36 ) $$Step 2 :
Rewrite $ z^{2}-36 $ as:
$$ z^{2}-36 = (z)^2 - (6)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = z $ and $ II = 6 $ , we have:
$$ z^{2}-36 = (z)^2 - (6)^2 = ( z-6 ) ( z+6 ) $$This page was created using
Polynomial Factoring Calculator