Hi Eulalie! Let's start with adding polynomials. Below is an example of how that will work. Notice that we are adding like terms. The 3x term is combined with the 4x term, the x2 term is combined with the 5x2 term and the 7 and 8 are added together.
(x2 +3x +7) + (5x2 +4x +8) = 6x2 + 7x +15
Subtracting works very similarly but it important to remember to distribute negative sign to every term of the polynomial that is being subtracted. Let's use the same polynomials as above but this time subtract the 2nd. The second step shows what I mean by distribute the negative sign.
(x2 +3x +7) - (5x2 +4x +8) = (x2 - 5x2) + (3x - 4x) + (7-8) = -4x2 -x -1
Lastly, lets look at multiplying polynomials. Every term in the first polynomial must be multiplied by every term in the second and the products are added as shown below. When multiplying two x terms, you add the superscripts (ex: x3 * x6 = x9). Like we did in the above examples, add/subtract like terms to simplify.
(4x + 2)(5x + 3) = (4x * 5x) + (4x * 3) + (2 * 5x) + (2 * 3) = 20x2 +12x +10x + 6 = 20x2 + 22x + 6
I hope this helps! Please reach out if you have any follow up questions.