Factor polynomial $$ 1029x^{3}y+24y^{4} $$
Answer
$$ 1029x^{3}y+24y^{4} = 3y(7x+2y)(49x^{2}-14xy+4y^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ 3y } $:
$$ 1029x^3y+24y^4 = 3y ( 343x^3+8y^3 ) $$Step 2 :
To factor $ 343x^{3}+8y^{3} $ we can use sum of cubes formula:
$$ I^3 + II^3 = (I + II) (I^2 - I \cdot II + II^2)$$After putting $ I = 7x $ and $ II = 2y $ , we have:
$$ 343x^{3}+8y^{3} = ( 7x+2y ) ( 49x^{2}-14xy+4y^{2} ) $$This page was created using
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