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

Given: Terms $3x^2-4y^2+5xy+20$ and $– x^2-y^2+6xy+20$.
 

To do: This is to find out what should be taken from $3x^2-4y^2+5xy+20$ to get $- x^2-y^2+6xy+20$.

Solution: Let us assume $a$ be the required term

Then,

$3x^2-4y^2+5xy+20-a=-x^2-y^2+6xy+20$

$a=3x^2-4y^2+5xy+20-(-x^2-y^2+6xy+20)$

$a=3x^2-4y^2+5xy+20+x^2+y^2-6xy-20$

$a=3x^2+x^2-4y^2+y^2+5xy-6xy+20-20$

$a=4x^2-3y^2-xy$

Therefore, $4x^2-3y^2-xy$ should be taken from $3x^2-4y^2+5xy+20$ to get $- x^2-y^2+6xy+20$.

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Updated on: 10-Oct-2022

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