Question

Let x and y be real numbers satisfying two conditions: x-y=5 and xy=7. Find x^3y+xy^3​

Answer 1

We can factor

$x^3y+xy^3 = xy(x^2+y^2) = xy[(x-y)^2+2xy]$

And now we know all the terms involved: substitute every occurrence of xy with 7 and every occurrence of x-y with 5 to have

$xy[(x-y)^2+2xy]=7\cdot(5^2+2\cdot 7) = 7\cdot (25-7) = 7\cdot 18 = 126$