Question
Factor polynomial $$ 8x^{6}-18x^{2} $$
Answer
$$ 8x^{6}-18x^{2} = 2x^{2}( 2x^{2}-3 )( 2x^{2}+3 ) $$
Explanation
Step 1 :
After factoring out $ 2x^{2} $ we have:
$$ 8x^{6}-18x^{2} = 2x^{2} ( 4x^{4}-9 ) $$Step 2 :
Rewrite $ 4x^{4}-9 $ as:
$$ 4x^{4}-9 = (2x^{2})^2 - (3)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 2x^{2} $ and $ II = 3 $ , we have:
$$ 4x^{4}-9 = (2x^{2})^2 - (3)^2 = ( 2x^{2}-3 ) ( 2x^{2}+3 ) $$This page was created using
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