Factor polynomial $$ 27x^{3}-216y^{3} $$
Answer
$$ 27x^{3}-216y^{3} = 27(x-2y)(x^{2}+2xy+4y^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 27 } $:
$$ 27x^3-216y^3 = 27 ( x^3-8y^3 ) $$Step 2 :
To factor $ x^{3}-8y^{3} $ 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 $ , we have:
$$ x^{3}-8y^{3} = ( x-2y ) ( x^{2}+2xy+4y^{2} ) $$This page was created using
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