Question
Factor polynomial $$ 625x^{4}-81 $$
Answer
$$ 625x^{4}-81 = ( 5x-3 )( 5x+3 )( 25x^{2}+9 ) $$
Explanation
Step 1 :
Rewrite $ 625x^{4}-81 $ as:
$$ 625x^{4}-81 = (25x^{2})^2 - (9)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 25x^{2} $ and $ II = 9 $ , we have:
$$ 625x^{4}-81 = (25x^{2})^2 - (9)^2 = ( 25x^{2}-9 ) ( 25x^{2}+9 ) $$Step 2 :
Rewrite $ 25x^{2}-9 $ as:
$$ 25x^{2}-9 = (5x)^2 - (3)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 5x $ and $ II = 3 $ , we have:
$$ 25x^{2}-9 = (5x)^2 - (3)^2 = ( 5x-3 ) ( 5x+3 ) $$This page was created using
Polynomial Factoring Calculator