What should be taken away from $3 x^{2} - 4 y^{2} + 5 x y + 20$ to obtain $- x^{2} - y^{2} + 6 x y + 20$ ?

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Solution

Mathematical operation with algebraic expressions.
Let us consider that $m$ should be taken away from $3 x^{2} - 4 y^{2} + 5 x y + 20$ to obtain $- x^{2} - y^{2} + 6 x y + 20$ .
$∴ (3 x^{2} - 4 y^{2} + 5 x y + 20) - m = - x^{2} - y^{2} + 6 x y + 20 \Rightarrow - m = - x^{2} - y^{2} + 6 x y + 20 - (3 x^{2} - 4 y^{2} + 5 x y + 20) \Rightarrow - m = - x^{2} - y^{2} + 6 x y + 20 - 3 x^{2} + 4 y^{2} - 5 x y - 20 \Rightarrow - m = - x^{2} - 3 x^{2} - y^{2} + 4 y^{2} + 6 x y - 5 x y + 20 - 20 \Rightarrow - m = - 4 x^{2} + 3 y^{2} + x y \Rightarrow m = - (- 4 x^{2} + 3 y^{2} + x y) \Rightarrow m = 4 x^{2} - 3 y^{2} - x y$
Hence, the expression $(4 x^{2} - 3 y^{2} - x y)$ should be taken away from $3 x^{2} - 4 y^{2} + 5 x y + 20$ to obtain $- x^{2} - y^{2} + 6 x y + 20$ .

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What should be subtracted from $3 x^{2} - 4 y^{2} + 5 x y + 20$ to obtain $- x^{2} - y^{2} + 6 x y + 20$ ?

What should be taken away from 3x² − 4y²+ 5xy + 20 to obtain

− x² − y²+ 6xy+ 20?

3 x^{2} - 4 y^{2} + 5 x y + 20

- x^{2} - y^{2} + 6 x y + 20

3 x^{2} - 4 y^{2} + 5 x y + 20

- x^{2} - y^{2} + 6 x y + 20

3 x^{2} - 4 y^{2} + 5 x y + 20

- x^{2} - y^{2} + 6 x y + 20

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