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