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