$(a)$ What should be added to $x^2+xy+y^2$ to obtain $2x^2+3xy$?
$(b)$ What should be subtracted from $2a+8b+10$ to get $-3a+7b+16$

Given: $(a)$ Terms $x^2+xy+y^2$ and $2x^2+3xy$.

$(b)$. Terms $2a+8b+10$ and $-3a+7b+16$

To do: $(a)$ This is to find out what should be added to $x^2+xy+y^2$ to obtain $2x^2+3xy$.

$(b)$ This is to find out what should be subtracted from $2a+8b+10$ to get $-3a+7b+16$

Solution: $(a)$. Let's assume $'a'$ to be the required term

$=a+(x^2+y^2+xy)=2x^2+3xy$

$a=2x^2+3xy-(x^2+y^2+xy)$

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

$a=x^2-y^2+2xy $

Therefore, $x^2-y^2+2xy$ should be added to $x^2+xy+y^2$ to obtain $2x^2+3xy$.

$(b)$. Let's assume $'p'$ to be the required term

$(2a+8b+10)-p=-3a+7b+16$

$p=2a+8b+10-(-3a+7b+16)$

$p=2a+8b+10+3a-7b-16$

$p=5a+b-6$

Therefore, $5a+b-6$ should be subtracted from $2a+8b+10$ to get $-3a+7b+16$.

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Updated on: 10-Oct-2022

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