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