In [1]:
import sympy as sym
import numpy as np
import math

from IPython.display import display, Math
from sympy.abc import w,x,y,z,a,b,c,d
sym.init_printing()
In [2]:
x**5 * x**3
Out[2]:
$$x^{8}$$
In [3]:
x**5 + x**3
Out[3]:
$$x^{5} + x^{3}$$
In [4]:
p1 = 4*x**2 - 2*x
p2 = x**3 - 1

p1*p2
Out[4]:
$$\left(4 x^{2} - 2 x\right) \left(x^{3} - 1\right)$$
In [5]:
sym.expand(p1*p2)
Out[5]:
$$4 x^{5} - 2 x^{4} - 4 x^{2} + 2 x$$
In [6]:
fxy = 4*x**4 - 9*y**3 - 3*x**2 + x*y**2
gxy = .8*y**3 - x**3 + 6*x**2*y

fxy
Out[6]:
$$4 x^{4} - 3 x^{2} + x y^{2} - 9 y^{3}$$
In [7]:
gxy
Out[7]:
$$- x^{3} + 6 x^{2} y + 0.8 y^{3}$$
In [8]:
display(Math('(%s) \\times (%s) = %s' %(sym.latex(fxy),sym.latex(gxy),sym.latex(sym.expand(fxy*gxy)))))
$\displaystyle (4 x^{4} - 3 x^{2} + x y^{2} - 9 y^{3}) \times (- x^{3} + 6 x^{2} y + 0.8 y^{3}) = - 4 x^{7} + 24 x^{6} y + 3 x^{5} + 3.2 x^{4} y^{3} - x^{4} y^{2} - 18 x^{4} y + 15 x^{3} y^{3} - 54 x^{2} y^{4} - 2.4 x^{2} y^{3} + 0.8 x y^{5} - 7.2 y^{6}$
In [9]:
xval = 5
yval = -2

fg = (fxy*gxy).subs({x:xval, y:yval})
print('Multiplied solutions is %s' %fg)

fxy_ans = fxy.subs({x:xval, y:yval})
gxy_ans = gxy.subs({x:xval, y:yval})

print('Separate solutions comes to %s' %(fxy_ans*gxy_ans))

Multiplied solutions is -1085833.80000000
Separate solutions comes to -1085833.80000000