a: \(\left(x+4\right)^2-2\left(x-5\right)\left(x+4\right)+\left(x-5\right)\)
\(=x^2+8x+16-2\left(x^2+4x-5x-20\right)+x-5\)
\(=x^2+9x+11-2x^2+2x+40=-x^2+11x+51\)
b: \(\left(16x^4-20x^2y^3-4x^5y\right):\left(-4x^2\right)\)
\(=\dfrac{-16x^4}{4x^2}+\dfrac{20x^2y^3}{4x^2}+\dfrac{4x^5y}{4x^2}\)
\(=-4x^2+5y^3+x^3y\)
c: \(15+x+\left(x-5\right)\left(2x+3\right)-2x\left(x-3\right)\)
\(=x+15+2x^2+3x-10x-15-2x^2+6x\)
=0
d: \(\left(2x-1\right)\left(x+3\right)-\left(x-2\right)^2-x\left(x+1\right)\)
\(=2x^2+6x-x-3-x^2+4x-4-x^2-x\)
=8x-7
e: \(\left(x-3\right)\left(x^2+3x+9\right)-x\left(x-2\right)\left(x+2\right)\)
\(=x^3-3^3-x\left(x^2-4\right)\)
\(=x^3-27-x^3+4x=4x-27\)
g: \(-2x\left(-3x+2\right)-\left(x+2\right)^2\)
\(=6x^2-4x-x^2-4x-4\)
\(=5x^2-8x-4\)
