Factor polynomial $$ 49p^{3}q-25pq^{3} $$
Answer
$$ 49p^{3}q-25pq^{3} = pq(7p+5q)(7p-5q) $$
Explanation
Step 1 :
Factor out common factor $ \color{blue}{ pq } $:
$$ 49p^3q-25pq^3 = pq ( 49p^2-25q^2 ) $$Step 2 :
Rewrite $ 49p^2-25q^2 $ as:
$$ \color{blue}{ 49p^2-25q^2 = (7p)^2 - (5q)^2 } $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 7p $ and $ II = 5q $ , we have:
$$ 49p^2-25q^2 = (7p)^2 - (5q)^2 = ( 7p-5q ) ( 7p+5q ) $$This page was created using
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