Question

Solve this question.

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Answer 1

A/Q
     3X^2+2XY-3Y^2+K=2X^2+3XY
⇒3X^2-2X^2+2XY-3XY-3Y^2+K=0
⇒X^2-XY-3Y^2+K=0
⇒K=-X^2+XY+3Y^2                   {ANSWER}

Answer 2

ANSWER (a)
Let the required expression be $A$. 
Now, 
$(3x^{2}+2xy-3y^{2})+A=(2x^{2}+3xy)$
⇒ $A=(2x^{2}+3xy)-(3x^{2}+2xy-3y^{2})$
      $=2x^{2}+3xy-3x^{2}-2xy+3y^{2}$
      $=2x^{2}-3x^{2}+3xy-2xy+3y^{2}$
      $=-x^{2}+xy+3y^{2}$
⇒ $A=-x^{2}+xy+3y^{2}$
∴ The required expression is $-x^{2}+xy+3y^{2}$. 

ANSWER (b)
Let the required expression be $A$. 
Now, 
$(3a+7b+8)-A=(-5a+3b+16)$
⇒ $(3a+7b+8)=(-5a+3b+16)+A$
⇒ $(-5a+3b+16)+A=(3a+7b+8)$
⇒ $A=(3a+7b+8)-(-5a+3b+16)$
      $=3a+7b+8+5a-3b-16$
      $=3a+5a+7b-3b+8-16$
      $=8a+4b-8$
⇒ $A=8a+4b-8$
∴ The required expression is $8a+4b-8$. 

Hope these may help you. 

If you have any doubt, then you can ask me in the comments.