\(F=\left(x^a+1\right)\left(x^a-2\right)-x^{a-2}\left(x^{a+2}-x^2\right)+2021\)
\(=x^{2a}-2x^a+x^a-2-x^{\left(a-2\right)+\left(a+2\right)}+x^{2+a-2}+2021\)
\(=x^{2a}-x^a-2-x^{2a}+x^a+2021\)
\(=\left(x^{2a}-x^{2a}\right)+\left(x^a-x^a\right)-2+2021\)
\(=2019\)
\(E=5x\left(x^2-7x+2\right)-x^2\left(5x-8\right)+27x^2-10x\)
\(=5x^3-35x^2+10x-5x^3+8x^2+27x^2-10x\)
\(=\left(5x^3-5x^3\right)+\left(-35x^2+8x^2+27x^2\right)+\left(10x-10x\right)\)
\(=0\)
\(D=\left(x^2-2\right)\left(x+2\right)-x^2\left(x+2\right)+2x\)
\(=x^3+2x^2-2x-4-x^3-2x^2+2x\)
\(=-4\)
\(C=\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+5\right)-\left(8-5x\right)\)
\(=x^3-2x^2+4x+2x^2-4x+8-x^3-5x-8+5x\)
\(=0\)
\(B=2x\left(x+3\right)-\left(x-1\right)\left(8+2x\right)\)
\(=2x^2+6x-8x-2x^2+8+2x\)
\(=8\)
\(A=3x\left(x+5\right)-\left(3x+18\right)\left(x-1\right)\)
\(=3x^2+15x-3x^2+3x-18x+18\)
\(=18\)