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