Factor polynomial $$ -x^{8}+81 $$
Answer
$$ -x^{8}+81 = ( -x^{2}+3 )( x^{2}+3 )( x^{4}+9 ) $$
Explanation
Step 1 :
Rewrite $ -x^{8}+81 $ as:
$$ -x^{8}+81 = 81 -x^8 = (9)^2 - (x^{4})^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 9 $ and $ II = x^{4} $ , we have:
$$ -x^{8}+81 = (9)^2 - (x^{4})^2 = ( -x^{4}+9 ) ( x^{4}+9 ) $$Step 2 :
Rewrite $ -x^{4}+9 $ as:
$$ -x^{4}+9 = 9 -x^4 = (3)^2 - (x^{2})^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 3 $ and $ II = x^{2} $ , we have:
$$ -x^{4}+9 = (3)^2 - (x^{2})^2 = ( -x^{2}+3 ) ( x^{2}+3 ) $$This page was created using
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