Question
Factor polynomial $$ 3x^{3}-24y^{6} $$
Answer
$$ 3x^{3}-24y^{6} = 3(x-2y^{2})(x^{2}+2xy^{2}+4y^{4}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 3 } $:
$$ 3x^3-24y^6 = 3 ( x^3-8y^6 ) $$Step 2 :
To factor $ x^{3}-8y^{6} $ we can use difference of cubes formula:
$$ I^3 - II^3 = (I - II) (I^2 + I \cdot II + II^2) $$After putting $ I = x $ and $ II = 2y^2 $ , we have:
$$ x^{3}-8y^{6} = ( x-2y^{2} ) ( x^{2}+2xy^{2}+4y^{4} ) $$This page was created using
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