a: \(\left(x+4\right)^2-\left(x^2-5x\right)\)
\(=x^2+8x+16-x^2+5x=13x+16\)
b: \(\left(4x-1\right)^2+15x^2+3x\)
\(=16x^2-8x+1+15x^2+3x\)
\(=31x^2-5x+1\)
c: \(5x^2-3x+2-\left(x+3\right)\left(x-3\right)\)
\(=5x^2-3x+2-\left(x^2-9\right)\)
\(=5x^2-3x+2-x^2+9=4x^2-3x+11\)
d: \(2x\left(x^2-3x-4\right)+\left(x+1\right)^3\)
\(=2x^3-6x^2-8x+x^3+3x^2+3x+1\)
\(=3x^3-3x^2-5x+1\)
e: \(-3x\left(x^2-5\right)+\left(x-1\right)^3\)
\(=-3x^3+15x+x^3-3x^2+3x-1\)
\(=-2x^3-3x^2+18x-1\)
f: \(x^3-2x^2-2x-10+\left(3x-2\right)^3\)
\(=x^3-2x^2-2x-10+27x^3-54x^2+36x-8\)
\(=28x^3-56x^2+34x-18\)
g: \(2x^2\left(3x^2-1\right)-\left(x^2-x-1\right)^2\)
\(=6x^4-2x^2-\left(x^4+x^2+1-2x^3-2x^2+2x\right)\)
\(=6x^4-2x^2-x^4+2x^3+x^2-2x-1=5x^4+2x^3-x^2-2x-1\)
h: \(-3x^4-2x^2+\left(x^2-2x-5\right)^2\)
\(=-3x^4-2x^2+x^4+4x^2+25-4x^3-10x^2+20x\)
\(=-2x^4-4x^3-8x^2+20x+25\)
