Question

consider the following polynomials. ab^2 +3ab+8a^2 and -5ab^2
Use the two polynomials to illustrate the following:
a. polynomials are closed under addition.
b. polynomials are closed under subtraction.
c. polynomials are closed under multiplication.


(can someone please explain and like evaluate the steps, I want to understand this.)

Answer 1

for multiplication, just expand out (ab^2 +3ab+8a^2)(-5ab^2)
every term in the product will have some combination of powers of a and b, so it will still be a polynomial.

same for addition and subtraction