Factor polynomial $$ 45z^{5}-125z^{3} $$
Answer
$$ 45z^{5}-125z^{3} = 5z^{3}( 3z-5 )( 3z+5 ) $$
Explanation
Step 1 :
After factoring out $ 5z^{3} $ we have:
$$ 45z^{5}-125z^{3} = 5z^{3} ( 9z^{2}-25 ) $$Step 2 :
Rewrite $ 9z^{2}-25 $ as:
$$ 9z^{2}-25 = (3z)^2 - (5)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 3z $ and $ II = 5 $ , we have:
$$ 9z^{2}-25 = (3z)^2 - (5)^2 = ( 3z-5 ) ( 3z+5 ) $$This page was created using
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