Question
Factor polynomial $$ 125c^{4}+cd^{3} $$
Answer
$$ 125c^{4}+cd^{3} = c(5c+d)(25c^{2}-5cd+d^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ c } $:
$$ 125c^4+cd^3 = c ( 125c^3+d^3 ) $$Step 2 :
To factor $ 125c^{3}+d^{3} $ we can use sum of cubes formula:
$$ I^3 + II^3 = (I + II) (I^2 - I \cdot II + II^2)$$After putting $ I = 5c $ and $ II = d $ , we have:
$$ 125c^{3}+d^{3} = ( 5c+d ) ( 25c^{2}-5cd+d^{2} ) $$This page was created using
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