# If when adding three polynomials,P+Q+R the result is 2x^2y and the polynomials P and Q are given by the expressions P=x^3+5xy^2+y^3,Q=y^3−10xy^2−x^3.

If when adding three polynomials, P+Q+R the result is $2{x}^{2}y$ and the polynomials P and Q are given by the expressions $P={x}^{3}+5x{y}^{2}+{y}^{3},Q={y}^{3}-10x{y}^{2}-{x}^{3}$. What is the expression for the polynomial R?
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casincal
Solution of the problem as follows
We have given three polynomials
$P={x}^{3}+5x{y}^{2}+{y}^{3}$
$Q={y}^{3}-10x{y}^{2}-{x}^{3}$
and $P+Q+R=2{x}^{2}y$
Then we have to final R.
$⇒P+Q+R=2{x}^{2}y$
$⇒{x}^{3}+{y}^{3}+5x{y}^{2}+{y}^{3}-{x}^{3}-10x{y}^{2}+R=2{x}^{2}y$
$⇒R=2{x}^{2}y-2{y}^{3}+5x{y}^{2}$