Giải thích các bước giải:

 a/.

$A+(5x^2-2xy)=6x^2+9xy-y^2$

⇔ $A=6x^2+9xy-y^2-(5x^2-2xy)$

⇔ $A=6x^2+9xy-y^2-5x^2+2xy$

⇔ $A=(6x^2-5x^2)+(9xy+2xy)-y^2$

⇒ $A=x^2+11xy-y^2$

b/.

$A-(3xy-4y^2)=x^2-7xy+8y^2$

⇔ $A=x^2-7xy+8y^2+(3xy-4y^2)$

⇔ $A=x^2-7xy+8y^2+3xy-4y^2$

⇔ $A=x^2+(8y^2-4y^2)+(-7xy+3xy)$

⇒  $A=x^2+4y^2-4xy$

⇒  $A=(x-2y)^2$

c/.

$(25x^2y-13xy^2+y^3)-A=11x^2-2y^3$

⇔ $A=(25x^2y-13xy^2+y^3)-(11x^2-2y^3)$

⇔ $A=25x^2y-13xy^2+(y^3+2y^3)-11x^2$

⇒ $A=25x^2y-13xy^2+3y^3-11x^2$

d/.

$(12x^4-15x ^2y+2xy^2+7)-A=0$

⇔ $A=12x^4-15x ^2y+2xy^2+7$

Đáp án:

$\begin{array}{l}
a)A + \left( {5{x^2} - 2xy} \right) = 6{x^2} + 9xy - {y^2}\\
 \Leftrightarrow A = 6{x^2} + 9xy - {y^2} - 5{x^2} + 2xy\\
 \Leftrightarrow A = {x^2} + 11xy - {y^2}\\
b)\\
A - \left( {3xy - 4{y^2}} \right) = {x^2} - 7xy + 8{y^2}\\
 \Leftrightarrow A = {x^2} - 7xy + 8{y^2} + 3xy - 4{y^2}\\
 \Leftrightarrow A = {x^2} - 4xy + 4{y^2}\\
c)\\
\left( {25{x^2}y - 13x{y^2} + {y^3}} \right) - A = 11{x^2} - 2{y^3}\\
 \Leftrightarrow A = 25{x^2}y - 13x{y^2} + {y^3} - 11{x^2} + 2{y^3}\\
 \Leftrightarrow A = 25{x^2}y - 13x{y^2} + 3{y^3} - 11{x^2}\\
d)\\
\left( {12{x^4} - 15{x^2}y + 2x{y^2} + 7} \right) - A = 0\\
 \Leftrightarrow A = 12{x^4} - 15{x^2}y + 2x{y^2} + 7
\end{array}$