Supplemental Worksheet Problems To Accompany: …€¦ · Section 15 – Adding and Subtracting Polynomials Page 1 Supplemental Worksheet Problems To Accompany: Math Video Tutor DVD
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
These are like terms because they each have an ‘x’ in them. Because of this, we can just add the coefficients. Since -2+3=1, the final answer is 1x, which is simply written as ‘x’.
These are unlike terms because one term contains a’ ’ and the other contains a . In order for two terms to be like terms, the variables and exponents in the terms must match exactly. Because of this, can’t add anything and so this expression is already simplified.
These are all like terms because they each have an ‘ ’ in them. Because of this, we can just add/subtract the coefficients. First, add the first two terms.
Next, subtract the final two terms since they are like terms as well.
In this case only the last two terms are like terms because those terms contain ’ in them. So, add the coefficients of the last two terms. We can’t do any further simplification because these remaining terms are unlike.
First, we notice that we can “distribute” the exponent in the first term inside the parenthesis. Do this first.
Since , rewrite the coefficient of the first term as ‘16’.
“Distribute” the exponent into the parenthesis of the second term. Remember when you raise an exponent to another exponent, you multiply the exponents.
Perform the multiplication in the exponent and rewrite as ‘9’.
These terms are like terms because each term has an in it. As a result, we can just subtract the coefficients.
We are subtracting two binomials here. Since the second binomial, (3b+5), is subtracted from the first, we need to distribute the implied “-1” into the second binomial.
Drop the first set of parenthesis.
We need to add like terms. ‘5b’ and ‘-3b’ are like terms because they each have a ‘b’. Add these terms. Since 5-3=2, the new coefficient of ‘b’ is ‘2’.
Next, perform the subtraction with the numbers. -7-5 = -12. Since the remaining terms are not like terms, they can’t be added further. We are done.
We are subtracting two binomials here. Since the second binomial, (2x+5y), is subtracted from the first, we need to distribute the implied “-1” into the second binomial.
Drop the first set of parenthesis.
We need to add like terms. ‘5x’ and ‘-2x’ are like terms because they each have a ‘x’. Add these terms. Since 5-2=3, the new coefficient of ‘x’ is ‘3’.
Now, “-8y” and “-5y” are also like terms. Combine these terms. Since -8-5 = -13, this is the new coefficient of ‘y’.
We are subtracting two trinomials here. Since the second trinomial is subtracted from the first, we need to distribute the implied “-1” into the second trinomial. You will end up multiplying each term in the second trinomial by “-1”.
Drop the first set of parenthesis.
We need to add like terms. Add with .
Add with .
Add “4” and “-7” together. All of these are unlike terms so we are done.