import sympy

a = sympy.Symbol('a')
b = sympy.Symbol('b')
x = sympy.Symbol('x')
y = sympy.Symbol('y')

a

$\displaystyle a$

f = a*x+b*y
f

$\displaystyle a x + b y$

f = a*(x+y)
f

$\displaystyle a \left(x + y\right)$

g = f.expand()
g

$\displaystyle a x + a y$

g.diff(x)

$\displaystyle a$

g.simplify()

$\displaystyle a \left(x + y\right)$

factor, collect are two other useful functions

g.subs({x:b})

$\displaystyle a b + a y$

h = g.subs({x:(3*b+5)})
h

$\displaystyle a y + a \left(3 b + 5\right)$

eq = []
eq.append(x+5*y)
eq.append(x-1)

solution = sympy.solve(eq,[x,y])
solution

{x: 1, y: -1/5}

i = x+5*y
j = i.subs(solution)
j

$\displaystyle 0$

type(j)

sympy.core.numbers.Zero

type(j.evalf(5))

sympy.core.numbers.Zero