Question
Factor polynomial $$ p^{4}-q^{4} $$
Answer
$$ p^{4}-q^{4} = (p^{2}+q^{2})(p+q)(p-q) $$
Explanation
Step 1 :
Rewrite $ p^4-q^4 $ as:
$$ \color{blue}{ p^4-q^4 = (p^2)^2 - (q^2)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = p^2 $ and $ II = q^2 $ , we have:
$$ p^4-q^4 = (p^2)^2 - (q^2)^2 = ( p^2-q^2 ) ( p^2+q^2 ) $$Step 2 :
Rewrite $ p^2-q^2 $ as:
$$ \color{blue}{ p^2-q^2 = (p)^2 - (q)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = p $ and $ II = q $ , we have:
$$ p^2-q^2 = (p)^2 - (q)^2 = ( p-q ) ( p+q ) $$This page was created using
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