VD4:
a: A+x^2-y^2=x^2-2y^2+3xy-2
=>A-y^2=-2y^2+3xy-2
=>A=-2y^2+3xy-2+y^2
=>A=-y^2+3xy-2
b: B-(5x^2-2xyz)=2x^2+2xyz+1
=>B=2x^2+2xyz+1+5x^2-2xyz
=>B=7x^2+1
Ví dụ 5:
a) Ta có: \(C=A+B\)
\(\Leftrightarrow C=\left(4x^2+3y^2-5xy\right)+\left(3x^2+2y^2+2x^2y^2\right)\)
\(\Leftrightarrow C=\left(4x^2+3x^2\right)+\left(3y^2+2y^2\right)-5xy+2x^2y^2\)
\(\Leftrightarrow C=7x^2+5y^2-5xy+2x^2y^2\)
b) Ta có: \(C+A=B\)
\(\Leftrightarrow C=B-A\)
\(\Leftrightarrow C=\left(3x^2+2y^2+2x^2y^2\right)-\left(4x^2+3y^2-5xy\right)\)
\(\Leftrightarrow C=3x^2+2y^2+2x^2y^2-4x^2-3y^2+5xy\)
\(\Leftrightarrow C=\left(3x^2-4x^2\right)+\left(2y^2-3y^2\right)+2x^2y^2+5xy\)
\(\Leftrightarrow C=-x^2-y^2+2x^2y^2+5xy\)