Factor polynomial $$ 49a^{5}b-4a^{3}b^{5} $$
Answer
$$ 49a^{5}b-4a^{3}b^{5} = a^{3}b(7a+2b^{2})(7a-2b^{2}) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ a^3b } $:
$$ 49a^5b-4a^3b^5 = a^3b ( 49a^2-4b^4 ) $$Step 2 :
Rewrite $ 49a^2-4b^4 $ as:
$$ \color{blue}{ 49a^2-4b^4 = (7a)^2 - (2b^2)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 7a $ and $ II = 2b^2 $ , we have:
$$ 49a^2-4b^4 = (7a)^2 - (2b^2)^2 = ( 7a-2b^2 ) ( 7a+2b^2 ) $$This page was created using
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