\(M\left(y\right)=y^2+y^3-3y+1-y^2+y^5-y^3+7y^5\)
\(M\left(y\right)=\left(y^2-y^2\right)+\left(y^3-y^3\right)+\left(-3y\right)+\left(y^5+7y^5\right)+1\)
\(M\left(y\right)=-3y+8y^5+1\)
\(\text{Sắp xếp theo lũy thừa giảm dần của biến:}\)
\(M\left(y\right)=8y^5-3y+1\)
\(N\left(y\right)=15y^3+5y^2-y^5-5y^2-4y^3-2y\)
\(N\left(y\right)=\left(15y^3-4y^3\right)+\left(5y^2-5y^2\right)+\left(-y^5\right)+\left(-2y\right)\)
\(N\left(y\right)=11y^3-y^5-2y\)
\(\text{Sắp xếp theo lũy thừa giảm dần của biến:}\)
\(N\left(y\right)=y^5-11y^3-2y\)
\(A\left(y\right)=M\left(y\right)+N\left(y\right)\)
\(A\left(y\right)=\left(8y^5-3y+1\right)+\left(y^5-11y^3-2y\right)\)
\(A\left(y\right)=8y^5-3y+1+y^5-11y^3-2y\)
\(A\left(y\right)=\left(8y^5+y^5\right)+\left(-3y-2y\right)+1+\left(-11y^3\right)\)
\(A\left(y\right)=9y^5-5y+1-11y^3\)
\(A\left(-1\right)=9.\left(-1\right)^5-5.\left(-1\right)+1-11.\left(-1\right)^3\)
\(A\left(-1\right)=\left(-9\right)-\left(-5\right)+1-\left(-11\right)\)
\(A\left(-1\right)=\left(-4\right)+1-\left(-11\right)\)
\(A\left(-1\right)=\left(-3\right)-\left(-11\right)=8\)
\(B\left(y\right)+M\left(y\right)=N\left(y\right)\)
\(\Rightarrow B\left(y\right)=N\left(y\right)-M\left(y\right)\)
\(\Rightarrow B\left(y\right)=\left(y^5-11y^3-2y\right)-\left(8y^5-3y+1\right)\)
\(\Rightarrow B\left(y\right)=y^5-11y^3-2y-8y^5+3y-1\)
\(\Rightarrow B\left(y\right)=\left(y^5-8y^5\right)+\left(-11y^3\right)+\left(-2y+3y\right)+\left(-1\right)\)
\(\Rightarrow B\left(y\right)=-7y^5-11y^3+y-1\)
