All Pre-Algebra Resources
Example Questions
Example Question #11 : Adding And Subtracting Polynomials
Simplify the following expression:
The simplify this expression, combine like terms. Terms are like if they have the same variables and powers. To combine them, use addition and/or subtraction of the coefficients. The variables and powers do not change when you are combining.
and are like terms (both have the variable ). To combine them, you do
6 and 2 are also like terms (both have no variable). To combine them, you do .
You now have your simplified expression: which is the final answer.
Example Question #12 : Polynomials
If and , what is ?
The first step is to write out as
The next step is to re-arrange the expression so it is ordered by exponential degree, as:
The final step is to sum together like terms and simplify the expression, as follows:
Example Question #13 : Polynomials
Simplify.
First distribute the negative:
Group like terms, meaning terms that have the same variable and same exponent:
Add the like terms:
Example Question #12 : Adding And Subtracting Polynomials
Simplify:
To solve you must first distribute the negative to the parentheses
Then you should combine like terms and you are left with
Example Question #15 : Polynomials
Simplify:
To simplify, we will combine like terms.
This has two terms with , and two terms with , so we will group those together:
Now we can add together the like terms. Remember that if a term doesn't have a coefficient [number in front of it], there is only one of them:
Example Question #16 : Polynomials
Simplify the following expression:
Combine the like terms (x's together and y's together).
Don't forget to distribute the negative sign through the parenthesis.
Example Question #17 : Polynomials
Subtract these polynomials:
Answer is not present.
Distribute appropriate sign and simplify:
Rearrange into standard form(descending degree or powers):
Example Question #18 : Adding And Subtracting Polynomials
Add the following polynomials:
Example Question #12 : Adding And Subtracting Polynomials
Simplify the expression.
When adding or subtracting polynomials with exponents, the value of the exponent never changes. The exponent does change when multiplying or dividing.
Start by categorizing each polynomial into groups according to the variable, then according to the like variable's exponent. Because and share a common variable AND exponent, you may add the coefficients:
However, because does not share the same variable, you may not subtract it from . Therefore, you leave the rest as is:
Example Question #13 : Adding And Subtracting Polynomials
Solve:
To simplify this expression, it is necessary to eliminate the parentheses grouping the terms. Distribute the negative signs. Double negative translate the sign to a positive.
The answer is .