Question
Factor polynomial $$ 216t^{6}+27y^{3} $$
Answer
$$ 216t^{6}+27y^{3} = 27(2t^{2}+y)(4t^{4}-2t^{2}y+y^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 27 } $:
$$ 216t^6+27y^3 = 27 ( 8t^6+y^3 ) $$Step 2 :
To factor $ 8t^{6}+y^{3} $ we can use sum of cubes formula:
$$ I^3 + II^3 = (I + II) (I^2 - I \cdot II + II^2)$$After putting $ I = 2t^2 $ and $ II = y $ , we have:
$$ 8t^{6}+y^{3} = ( 2t^{2}+y ) ( 4t^{4}-2t^{2}y+y^{2} ) $$This page was created using
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