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© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 1
Supplemental Worksheet Problems To Accompany:
Math Video Tutor DVD – Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Please watch Section 15 of this DVD before working these problems.
The DVD is located at:
http://www.mathtutordvd.com/products/item8.cfm
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 2
1) Simplify the expression, if possible.
2) Simplify the expression, if possible.
3) Simplify the expression, if possible.
4) Simplify the expression, if possible.
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 3
5) Simplify the expression, if possible.
6) Simplify the expression, if possible.
7) Simplify the expression, if possible.
8) Simplify the expression, if possible.
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 4
9) Simplify the expression, if possible.
10) Perform the indicated operation and simplify.
11) Perform the indicated operation and simplify.
12) Perform the indicated operation and simplify.
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 5
13) Perform the indicated operation and simplify.
14) Perform the indicated operation and simplify.
15) Perform the indicated operation and simplify.
16) Perform the indicated operation and simplify.
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 6
17) Perform the indicated operation and simplify.
18) Perform the indicated operation and simplify.
19) Perform the indicated operation and simplify.
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 7
Question
Answer
1) Simplify the expression, if possible.
Begin.
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’.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 8
Question
Answer
2) Simplify the expression, if possible.
Begin.
These are like terms because they each have an ‘ ’ in them. Because of this, we can just add the coefficients.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 9
Question
Answer
3) Simplify the expression, if possible.
Begin.
These are like terms because they each have an ‘ ’ in them. Because of this, we can just subtract the coefficients.
Ans: 18xy2
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 10
Question
Answer
4) Simplify the expression, if possible.
Begin.
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.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 11
Question
Answer
5) Simplify the expression, if possible.
Begin.
These are like terms because they each have an ‘ ’ in them. Because of this, we can just subtract the coefficients.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 12
Question
Answer
6) Simplify the expression, if possible.
Begin.
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.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 13
Question
Answer
7) Simplify the expression, if possible.
Begin.
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.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 14
Question
Answer
8) Simplify the expression, if possible.
Begin.
First, we notice that we can “distribute” the exponent in the first term inside the parenthesis.
Now all terms are like terms because all terms have a in them. Add the first two terms.
Since these terms are also like, subtract the final two terms.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 15
Question
Answer
9) Simplify the expression, if possible.
Begin.
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.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 16
Question
Answer
10) Perform the indicated operation and simplify.
Begin.
We are adding two binomials here. Since they are just added together, we can drop the parenthesis.
We need to add like terms. ‘2y’ and ‘4y’ are like terms because they each have a ‘y’. Add these terms.
Next, add the numbers together. Since ‘6y’ and ‘4’ are not like terms, they can’t be added further. We are done.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 17
Question
Answer
11) Perform the indicated operation and simplify.
Begin.
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.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 18
Question
Answer
12) Perform the indicated operation and simplify.
Begin.
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’.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 19
Question
Answer
13) Perform the indicated operation and simplify.
Begin.
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.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 20
Question
Answer
14) Perform the indicated operation and simplify.
Begin.
We are adding two trinomials here. We can drop all parenthesis.
We need to add like terms. Add with .
Add with .
Add “-2” and “2” together. All of these remaining terms are unlike terms so we are done.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 21
Question
Answer
15) Perform the indicated operation and simplify.
Begin.
First, distribute the ‘5’ into the first set of parenthesis.
Distribute the ‘7’ into the second set of parenthesis.
We need to add like terms. Add with .
Add with . These remaining terms are unlike terms so we are done.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 22
Question
Answer
16) Perform the indicated operation and simplify.
Begin.
First, distribute the ‘-4’ into the first set of parenthesis.
Distribute the ‘-5’ into the second set of parenthesis.
We need to add like terms. Add with .
Add with . These remaining terms are unlike terms so we are done.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 23
Question
Answer
17) Perform the indicated operation and simplify.
Begin.
2x3 + 2x2 − 3x + 5+ 3x3 − 4x2 − x − 7
Since we are just adding these polynomials, we can drop the parenthesis and begin to look for like terms to add together.
Add and
Add with .
Add with .
Add ‘5’ with ‘-7’.
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 24
Question
Answer
18) Perform the indicated operation and simplify.
Begin.
Since we are just adding these polynomials, we can drop the parenthesis and begin to look for like terms to add together.
Add and
Add with .
Add with .
Ans:
© 2008 Jason Gibson / MathTutorDVD.com Math Video Tutor Fractions Thru Algebra Section 15 – Adding and Subtracting Polynomials
Page 25
Question
Answer
19) Perform the indicated operation and simplify.
Begin.
Since we are subtracting one polynomial from the other, distribute the implied “-1” into the second polynomial.
Drop the first set of parenthesis.
Add and
Add with .
Add with .
Ans: