Factor polynomial $$ w^{4}-625 $$
Answer
$$ w^{4}-625 = ( w-5 )( w+5 )( w^{2}+25 ) $$
Explanation
Step 1 :
Rewrite $ w^{4}-625 $ as:
$$ w^{4}-625 = (w^{2})^2 - (25)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = w^{2} $ and $ II = 25 $ , we have:
$$ w^{4}-625 = (w^{2})^2 - (25)^2 = ( w^{2}-25 ) ( w^{2}+25 ) $$Step 2 :
Rewrite $ w^{2}-25 $ as:
$$ w^{2}-25 = (w)^2 - (5)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = w $ and $ II = 5 $ , we have:
$$ w^{2}-25 = (w)^2 - (5)^2 = ( w-5 ) ( w+5 ) $$This page was created using
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