Here are 5-easy steps to multiply polynomials! Also there are Example Questions if the written steps are to hard for you to understand.
Before We Begin You Need To Know The Vocabulary:
Constant: It is the number which is after the variable like it is adding, subtracting, dividing, and multiplying to the term. (4p+6)
Term: A polynomial term have variables to whole-number exponents; there are no square roots of exponents, no fractional powers.
Example: 4p² is a polynomial term.
4p-² is not a polynomial. This has a negative exponent!
Okay Lets Begin Math Pirates!
Example Question: (4p+6)(2+4p)
Step 1. Multiply the first digit & variable in the first term to the first digit of the second term.
Example: (4p+6)(2+4p) 4p x 2 = 8p
Step 2. Then multiply the same digit from the first term to the digit from the second term.
Example: (4p+6)(2+4p) 4 x 4 = 16
You notice that we haven't did nothing about the variable ( p). To multiply the variables correctly please read on. If you already know how please go to the next step 3.
To Multiply Variables To multiply variables it's pretty simple. If your multiplying variables that already exist and are the same imaging there is a little one on top of that certain variable such as (p¹) The little one is just to help you how many of that variable is there before we are multiplying them together. In this case it is the variable "p". To multiply the variables, in this case the variable is "p". Just add the little ones together and that is how to multiply the varibles. p¹+p¹=p². If you got variables such as (3JKL+4JKL) it should look like this (3J²K²L²). It doesn't really matter what variables you got just remember that there is a little one on top of each variable and just add the little ones together. You should get 16p²
Step 3. Take the constant number which in this case is (+6). Now take the constant from the first term and multiply the other constant from the other term.
Example: (4p+6)(2+4p) 6x2=12
Step 4. Almost Finish! Take the same constant from the first polynomial and multiply it with the number coefficient and the variable from the second polynomial.
Example: (4p+6)(2+4p) 6x4=24 and just add the variable "p" 24p
Step 5. Last Step! After doing all the multiplying, here comes the easy part you just combine any like terms and then put your answer in ascending order.
Example: 24p + 8p 24+8=32
24p+8p add the variables together p¹+p¹=p²
Your Final Answer: 32p²
There you have it! That is how you multiply polynomials! If I have missed anything please comment and ill reply soon as possible!
Hope these steps helped you how to multiply polynomials! Good Luck!! :)