Factor polynomial $$ 125r^{3}s-64s^{4} $$
Answer
$$ 125r^{3}s-64s^{4} = s(5r-4s)(25r^{2}+20rs+16s^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ s } $:
$$ 125r^3s-64s^4 = s ( 125r^3-64s^3 ) $$Step 2 :
To factor $ 125r^{3}-64s^{3} $ we can use difference of cubes formula:
$$ I^3 - II^3 = (I - II) (I^2 + I \cdot II + II^2) $$After putting $ I = 5r $ and $ II = 4s $ , we have:
$$ 125r^{3}-64s^{3} = ( 5r-4s ) ( 25r^{2}+20rs+16s^{2} ) $$This page was created using
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