Factor polynomial $$ 6m^{4}-96 $$
Answer
$$ 6m^{4}-96 = 6( m-2 )( m+2 )( m^{2}+4 ) $$
Explanation
Step 1 :
After factoring out $ 6 $ we have:
$$ 6m^{4}-96 = 6 ( m^{4}-16 ) $$Step 2 :
Rewrite $ m^{4}-16 $ as:
$$ m^{4}-16 = (m^{2})^2 - (4)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = m^{2} $ and $ II = 4 $ , we have:
$$ m^{4}-16 = (m^{2})^2 - (4)^2 = ( m^{2}-4 ) ( m^{2}+4 ) $$Step 3 :
Rewrite $ m^{2}-4 $ as:
$$ m^{2}-4 = (m)^2 - (2)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = m $ and $ II = 2 $ , we have:
$$ m^{2}-4 = (m)^2 - (2)^2 = ( m-2 ) ( m+2 ) $$This page was created using
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