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$(a)$ 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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