a: \(\left(x-1\right)\left(x+2\right)\)
\(=x^2+2x-x-2\)
\(=x^2+x-2\)
b: \(\left(3+x\right)\left(x+1\right)\)
\(=\left(x+3\right)\left(x+1\right)\)
\(=x^2+x+3x+3\)
\(=x^2+4x+3\)
c: \(\left(3x^2-4\right)\left(x+3\right)\)
\(=3x^2\cdot x+3x^2\cdot3-4\cdot x-4\cdot3\)
\(=3x^3+9x^2-4x-12\)
d: \(\left(3x+5\right)\left(2x-7\right)\)
\(=6x^2-21x+10x-35\)
\(=6x^2-11x-35\)