Question
Factor polynomial $$ 375x^{3}+1029y^{3} $$
Answer
$$ 375x^{3}+1029y^{3} = 3(5x+7y)(25x^{2}-35xy+49y^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 3 } $:
$$ 375x^3+1029y^3 = 3 ( 125x^3+343y^3 ) $$Step 2 :
To factor $ 125x^{3}+343y^{3} $ we can use sum of cubes formula:
$$ I^3 + II^3 = (I + II) (I^2 - I \cdot II + II^2)$$After putting $ I = 5x $ and $ II = 7y $ , we have:
$$ 125x^{3}+343y^{3} = ( 5x+7y ) ( 25x^{2}-35xy+49y^{2} ) $$This page was created using
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