a/\(F\left(x\right)=-4x^2+7-6x+5x^3\)
\(=5x^3-4x^2-6x+7\)
\(G\left(x\right)=4x^2+9x-2x^4+4x^3-12\)
\(=-2x^4+4x^3+4x^2+9x-12\)
b/\(F\left(x\right)+G\left(x\right)=\left(5x^3-4x^2-6x+7\right)+\left(-2x^4+4x^3+4x^2+9x-12\right)\)
\(=5x^3-4x^2-6x+7-2x^4+4x^3+4x^2+9x-12\)
\(=\left(5x^3+4x^3\right)-\left(4x^2-4x^2\right)+\left(-6x+9x\right)-2x^4-\left(-7+12\right)\)
\(=9x^3-0+3x-2x^4-5\)
\(=9x^3+3x-2x^4-5\)