Question
Factor polynomial $$ p^{6}q^{4}-q^{7} $$
Answer
$$ p^{6}q^{4}-q^{7} = q^{4}(p^{2}-q)(p^{4}+p^{2}q+q^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ q^4 } $:
$$ p^6q^4-q^7 = q^4 ( p^6-q^3 ) $$Step 2 :
To factor $ p^{6}-q^{3} $ we can use difference of cubes formula:
$$ I^3 - II^3 = (I - II) (I^2 + I \cdot II + II^2) $$After putting $ I = p^2 $ and $ II = q $ , we have:
$$ p^{6}-q^{3} = ( p^{2}-q ) ( p^{4}+p^{2}q+q^{2} ) $$This page was created using
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