Problem $1$: Multiplication of Polynomial Texts $($hw$0\_$p$1.$py $)$

In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves

only the operations of addition, subtraction, multiplication, and non$-$negative integer exponents of

variables. An example of a polynomial of a single variable $x,$ is $x^2-4x+7.$ An example in three

variables is $x^3+2x^{5}Y{Z}^2-YZ+1.$

In this homework, your task is to write a program to allow a text$-$version multiplication of multiple

polynomials. Specifically, the user is allowed to input a string that represents the multiplication of

several polynomials. Then you program needs to generate the string of the resulting polynomials.

The input and output polynomial strings need to follow the following rules.

$(1)n*x$ means $n$ is the coefficient, $x$ is the variable, and $n$ is the coefficient of variable $x.$ In

other words, coefficients are always placed before variables.

$(2)x^n$ represents $x^n,$ where $x$ is the variable, and $n$ is the exponent of $x.$ That said,

exponents are always placed after variables.

$(3)$ Polynomials with the same variables need to be put together by adding their coefficients, for

example, $5*x{Y}^2+3*x{Y}^2$ should be $8*x{Y}^2.$

Note that you can use only pure Python, i$.$e$.,$ you cannot use any package.

Sample Input$/$Output:

c: $\backslash$Python$35\backslash$workspace$\backslash 20181$ hw$3>$hw$3\_$p$2.$py

Input the polynomials: $(x+2Y)(2x2-Y2+Z)$

Output Result: $2x3-xY2+xZ+4x2Y-2Y3+2YZ$

C: $\backslash$Py thon$353$ workspace $\backslash 2018\backslash$hw$3>$hw$3$

p$2.$py

Input the polynomials: $(2x+3Y+4Z)(xY2+x2Y+Z2)$

Dutput Result: $5x2Y2+2x3Y+2xZ2+3xY3+3YZ2+4xY2Z+4x2YZ+4Z3$

C: $\backslash$Python$35\backslash$workspace$\backslash 2018\backslash$hw$3>$hw$3$

p$2.$py

Input the polynomials: $(A+2B2)(B+3C3)(2A+B+C)$

Output Result: $2A2B+AB2+$ABC$+6AC_3+3$ABC$3+3AC4+4AB3+2B4+2B3C+12ABC_3+6BC_3+6B2C4$

FAQ

The polynomials entered in the first question need to be enclosed in $"()"$ eg $($X$)($X$^2+$Y$^3)$