Question
Factor polynomial $$ 4w^{5}-4w $$
Answer
$$ 4w^{5}-4w = 4w( w-1 )( w+1 )( w^{2}+1 ) $$
Explanation
Step 1 :
After factoring out $ 4w $ we have:
$$ 4w^{5}-4w = 4w ( w^{4}-1 ) $$Step 2 :
Rewrite $ w^{4}-1 $ as:
$$ w^{4}-1 = (w^{2})^2 - (1)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = w^{2} $ and $ II = 1 $ , we have:
$$ w^{4}-1 = (w^{2})^2 - (1)^2 = ( w^{2}-1 ) ( w^{2}+1 ) $$Step 3 :
Rewrite $ w^{2}-1 $ as:
$$ w^{2}-1 = (w)^2 - (1)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = w $ and $ II = 1 $ , we have:
$$ w^{2}-1 = (w)^2 - (1)^2 = ( w-1 ) ( w+1 ) $$This page was created using
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