The sum of two polynomials is $3 x^{2} + 2 x y - y^{2}$ . Determine the other polynomial if one of them is $2 x^{2} + 3 y^{2}$ .

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Solution

Let the two polynomials be P and G whose sum is F.
Let F = $3 x^{2} + 2 x y - y^{2}$
and G = $2 x^{2} + 3 y^{2}$

According to the question, F = G + P
Therefore, P = F - G
=> P = F - G
=> P = $(3 x^{2} + 2 x y - y^{2}) - (2 x^{2} + 3 y^{2})$
=> P = $(3 - 2) x^{2} + (- 1 - 3) y^{2} + 2 x y$
=> P = $x^{2} - 4 y^{2} + 2 x y$

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The sum of two polynomials is 3x2+2xy−y2. Determine the other polynomial if one of them is 2x2+3y2.

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The sum of two polynomials is $3 x^{2} + 2 x y - y^{2}$ . Determine the other polynomial if one of them is $2 x^{2} + 3 y^{2}$ .