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

− x² − y²+ 6xy + 20?

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Solution

Let p be the required term.

(3x² − 4y² + 5xy + 20) − p = − x² − y² + 6xy + 20

p = (3x² − 4y² + 5xy + 20) − (− x² − y² + 6xy + 20)

= 3x² − 4y² + 5xy + 20 + x² + y² − 6xy − 20

= 3x² + x²− 4y² + y² + 5xy − 6xy + 20 − 20

= 4x² − 3y² − xy

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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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Question 5

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

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