SOLUTION: If x+y=a and xy=b, find the value of {{{x^2y+xy^2+x^2+y^2}}}
I know that you have to square root {{{x^2+y^2}}} and {{{xy^2}}} to find b and a, but I'm not really sure what else
Algebra ->
Polynomials-and-rational-expressions
-> SOLUTION: If x+y=a and xy=b, find the value of {{{x^2y+xy^2+x^2+y^2}}}
I know that you have to square root {{{x^2+y^2}}} and {{{xy^2}}} to find b and a, but I'm not really sure what else
Log On
Question 888735: If x+y=a and xy=b, find the value of
I know that you have to square root and to find b and a, but I'm not really sure what else to do. Thanks! Found 2 solutions by Fombitz, Edwin McCravy:Answer by Fombitz(32388) (Show Source):
We have to get that expression in terms of a and b,
Since a is the sum of x and y and b is the product of x and y,
we look for ways to get the sum a=x+y and the product b=xy.
Looking at this:
We notice that the first two terms factor as xy(x+y)
which immediately becomes ba
We look at the last two terms.
Since , we notice that those last two
terms will be if we add 2xy between them, but
if we do that we'll have to subtract 2xy to offset, so we
do that:
Factor the middle three terms as .
Finally, we substitute a for x+y and b for xy, and we end up with
Edwin
