\(1,\\ A+B=4x^2-5xy+3y^2+3x^2+5xy+y^2\\ A+B=7x^2+4y^2\\ 2,\\ a,M=6x^2+9xy-y^2-5x^2+2xy\\ M=x^2+11xy-y^2\\ b,M=x^2-7xy+8y^2+3xy-4y^2\\ M=x^2-4xy+4y^2\)
\(6,\\ a,f\left(x\right)=8x^2-6x-2=0\\ \Leftrightarrow\left(x-1\right)\left(4x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{4}\end{matrix}\right.\\ b,h\left(x\right)=7x^2+11x+4=0\\ \Leftrightarrow\left(7x+4\right)\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{4}{7}\\x=-1\end{matrix}\right.\\ c,g\left(x\right)=x\left(x-10\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=10\end{matrix}\right.\)
\(A+B=4x^2-5xy+3y^2+3x^2+5xy+y^2\)
\(=7x^2+4y^2\)
\(A-B=4x^2-5xy+3y^2-3x^2-5xy-y^2\)
\(=x^2-10xy+2y^2\)
\(4,\\ a,P=M+N=-xy^2+3x^2y-x^2y^2+\dfrac{1}{2}x^2y-xy^2-\dfrac{2}{3}x^2y^2\\ P=-2xy^2+\dfrac{7}{2}x^2y-\dfrac{5}{3}x^2y^2\\ Q=N-M=\dfrac{1}{2}x^2y-xy^2-\dfrac{2}{3}x^2y^2+xy^2-3x^2y+x^2y^2\\ Q=-\dfrac{5}{2}x^2y+\dfrac{1}{3}x^2y^2\\ c,Q=-\dfrac{5}{2}\left(-1\right)^2\cdot\dfrac{1}{2}+\dfrac{1}{3}\left(-1\right)^2\cdot\left(\dfrac{1}{2}\right)^2\\ Q=-\dfrac{5}{4}+\dfrac{1}{12}=-\dfrac{7}{6}\)
