Explain how you know which terms in different polynomial scan be added or subtracted. What do you add or subtract?

Question

We are learning binomials and trinomials

Answer 1

Polynomials are made up of one or more terms. These terms are separated by the addition and subtraction signs in the examples you'll learn about. You can add and subtract polynomials by first placing like terms next to each other and then adding/subtracting them. If a term is negative, meaning that a - comes before it, make sure that you keep that - with the term.

For example:

5x² + 2x - 6 has three terms, 5x², 2x, and -6 (this is a trinomial, "tri" for three parts)

 

3x² + 10 has two terms, 3x² and 10 (this is a binomial, "bi" for two parts)

 

If you want to add these two polynomials together you first want to place the like terms, or parts, next to each other. Terms are alike if they have the same variables (x, y, z, etc. or even xy or xyz, as long as they're the same) and the same exponents ( the ² in this case).

 

So, you end up with:

5x² + 3x² , 2x , and -6 + 10

 

The exponents stay the same in addition and subtraction so you get

 

(5+3)x² + 2x + (-6+10)

 

which is equal to:

 

8x² + 2x + 4

 

 

Let me know if you still need some help or if you have any specific problems that you want me to explain for you!

Answer 2

The variables must be exactly the same

in order to add or subtract the terms.

 

8x+2x = 10x

 

8x² + 3x² + 5x = 11x² + 5x

we cannot add x² to x because they are

not the same exact variable.

 

6x - x + y = 5x + y

We can subtract one x from 6x but we cannot

combine the y with that because it is a different

variable.

 

5xy²-10-3x³y-2xy²+6x³y² - 8 =

 

5xy²-2xy² + 6x³y²-3x³y-10-8 =

 

3xy² + 6x³y² - 3x³y - 18

we have combined all the terms that have

the exact same variables and also added

the constants (regular numbers...)