1) Evaluate each algebraic expression, given that x= -1, y=3, z=2, a =1/2, b= -2/3. a) b)c)
2) Determine the degree of each of the following polynomials. a) b) c)
3) Remove the symbols of grouping and simplify the resulting expressions by combining like terms. a) (x + 3y – z) – (2y – x +3z) + (4z – 3x +2y)
b)
c) 3 – {2x – [1 –(x +y)] + [x – 2y]}
4) Add the algebraic expressions in each of the following groups. a)
b)
5) Subtract the algebraic expressions in each of the following groups. a)
b)

6) Evaluate each algebraic expression, given that x= -1, y=3, z=2, a =1/2, b= -2/3. b) b)c)
7) Determine the degree of each of the following polynomials. b) b) c)
8) Remove the symbols of grouping and simplify the resulting expressions by combining like terms. d) (x + 3y – z) – (2y – x +3z) + (4z – 3x +2y)
e)
f) 3 – {2x – [1 –(x +y)] + [x – 2y]}
9) Add the algebraic expressions in each of the following groups. c)
d)
10) Subtract the algebraic expressions in each of the following groups. c)
d)

11) Evaluate each algebraic expression, given that x= -1, y=3, z=2, a =1/2, b= -2/3. c) b)c)
12) Determine the degree of each of the following polynomials. c) b) c)
13) Remove the symbols of grouping and simplify the resulting expressions by combining like terms. g) (x + 3y – z) – (2y – x +3z) + (4z – 3x +2y)
h)
i) 3 – {2x – [1 –(x +y)] + [x – 2y]}
14) Add the algebraic expressions in each of the following groups. e) f)
15) Subtract the algebraic expressions in each of the following groups. e)
f)

...Algebra is a way of working with numbers and signs to answer a mathematical problem (a question using numbers)
As a single word, "algebra" can mean[1]:
* Use of letters and symbols to represent values and their relations, especially for solving equations. This is also called "Elementary algebra". Historically, this was the meaning in pure mathematics too, like seen in "fundamental theorem of algebra", but not now.
* In modern pure mathematics,
* a major branch of mathematics which studies relations and operations. It's sometimes called abstract algebra, or "modern algebra" to distinguish it from elementary algebra.
* a mathematical structure as a "linear" ring, is also called "algebra," or sometimes "algebra over a field", to distinguish it from its generalizations.
A variable is a letter or symbol that takes place of a number in Algebra. Common symbols used are a, x, y, θ, and λ. The letters x and y are commonly used, but remember that any other symbols would work just as well.
Variables are used in algebra as placeholders for unknown numbers. If you see "3 + x", don't panic! All this means is that we are adding a number who's value we don't yet know.
Term: A term is a number or a variable or the product of a number and a variable(s).
An expression is two or more terms, with operations...

...ALGEBRA
In all three of these problems there is use of all of the terms required: simplify, like terms, coefficient, distribution, and removing parentheses. There is also use with the real number properties of the commutative property of addition and the commutative property of multiplication. In what ways are the properties of real numbers useful for simplifying algebraic expression? The properties are useful for identifying what should go where and with what, to make it simpler to understand and to solve the equation properly. When we break things down to a simplified process, it is much easier to see how the real numbers are placed and why they are placed that way. Real numbers do not actually show the value of something real in the “real world”. For example, in mathematics if we write 0.5 we mean exactly half, but in the real world half may not be exactly half. In all reality, we use mathematics every single day, whether we consciously realize it or not. Math is the key subject that applies to our everyday lives in the “real world”.
Expression number one like terms are combined by adding coefficients, the removal of parentheses, and the use of commutative property of addition and multiplication. Expression number two has the use of quite a bit of distribution, combining like terms, and removal of parentheses. Expression number three like terms are combined by adding coefficients also. In this expression there is a temporary addition of...

...Pre-Calculus—Prerequisite Knowledge &Skills
III. Polynomials
A. Exponents
The expression bn is called a power or an exponential expression.
This is read “b to the nth power”
The b is the base, and the small raised symbol n is called the exponent.
The exponent indicates the number of times the base occurs as a factor.
Examples—Express each of the following using exponents.
a. 5 x 5 x 5 x 5 x 5 x 5 x 5 =
b. 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 =
c. 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 =
The powers of a number b can be written in factored form or in exponential form.
Factored Form Exponential Form
First power of b b b (= b1) “b to the first power”
(we normally do not write the 1 for a first power—it is just understood)
Second power of b b x b b2 “b to the second power”,
or “b squared”
Third power of b b x b x b b3 “b to the third power”,
or “b cubed”
Fourth power of b b x b x b x b b4 “b to the fourth power”
Example—Evaluate x3 if x = – 2
Example—Evaluate if x = 2
B. Adding and Subtracting Polynomials
Examples of Monomials 7 h –8x2y
A monomial is an expression that is either a number, a variable, or is a product of a numeral and one or more variables. Monomials (such as 7) that consist of only a number with no variables are...

...
Solving Proportions
Intermediate Algebra
Math 222
Professor Wick
February 9, 2013
For this week’s assignment we had to solve problem 56 on page number 437. This particular question is about solving a proportion. Proportions are any statement expressing the equality of two ratios. The proportion can be written out as a/b = c/d . In any proportion the numbers in the positions of a and d shown here are called the extremes. The numbers in the positions of b and c as shown are called the means (Dugopolski, 2012). The question is asked in regards to a bear population. Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population? For this proportion, I noted 50/100 = 2/x. The means are 100 and 2, and the extremes are 50 and x. In order to solve for x, I need to cross multiply 100 * 2 = 200. Hence, x = 200. Based on my calculations, I can only conclude that the conservationists may estimate that the bear population increased over the last year from 50 to 200.
For the next part of my assignment I will try to solve this equation involving x and y. First I will solve for x.
y-1/ x+3 = -3/4
Multiply both sides of the equation by (x+3).
(y−1)=−3/4⋅(x+3))
Remove the extra parentheses....

...HISTORY OF ALGEBRAAlgebra may divided into "classical algebra" (equation solving or "find the unknown number" problems) and "abstract algebra", also called "modern algebra" (the study of groups, rings, and fields). Classical algebra has been developed over a period of 4000 years. Abstract algebra has only appeared in the last 200 years.
The development of algebra is outlined in these notes under the following headings: Egyptian algebra, Babylonian algebra, Greek geometric algebra, Diophantine algebra, Hindu algebra, Arabic algebra, European algebra since 1500, and modern algebra. Since algebra grows out of arithmetic, recognition of new numbers - irrationals, zero, negative numbers, and complex numbers - is an important part of its history.
The development of algebraic notation progressed through three stages: the rhetorical (or verbal) stage, the syncopated stage (in which abbreviated words were used), and the symbolic stage with which we are all familiar.
The materials presented here are adapted from many sources including Burton, Kline's Mathematical Development From Ancient to Modern Times, Boyer's A History of Mathematics , and the essay on "The History of Algebra" by Baumgart in Historical Topics for the...

... alone.
= 5 The answer after simplifying.
+ -
3 - x – 5 The final answer.
In conclusion, I have found polynomials are very beneficial to one’s daily life. The use of algebraic functions is very common without individuals actually knowing it. It makes handling business matters easier. When an individual wants to learn about investing or saving, polynomials will be an easy way to receive the exact amount time and what you will need to reach your goals. Until this class, I would have never known how important algebra can be to one’s daily life. Once I began the logics it began to make sense. Now I plan to use this formula normally from this day forward.
...

...Unlike geometry, algebra was not developed in Europe. Algebra was actually discovered (or developed) in the Arab countries along side geometry. Many mathematicians worked and developed the system of math to be known as the algebra of today. European countries did not obtain information on algebra until relatively later years of the 12th century. After algebra was discovered in Europe, mathematicians put the information to use in very remarkable ways. Also, algebraic and geometric ways of thinking were considered to be two separate parts of math and were not unified until the mid 17th century.
The simplest forms of equations in algebra were actually discovered 2,200 years before Mohamed was born. Ahmes wrote the Rhind Papyrus that described the Egyptian mathematic system of division and multiplication. Pythagoras, Euclid, Archimedes, Erasasth, and other great mathematicians followed Ahmes ("Letters"). Although not very important to the development of algebra, Archimedes (212BC 281BC), a Greek mathematician, worked on calculus equations and used geometric proofs to prove the theories of mathematics ("Archimedes").
Although little is known about him, Diophantus (200AD 284AD), an ancient Greek mathematician, studied equations with variables, starting the equations of algebra that we know today. Diophantus is often known as the "father of...

...Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis.
For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers.
• As a single word without article, "algebra" names a broad part of mathematics (see below).
• As a single word with article or in plural, "algebra" denotes a specific mathematical structure. Seealgebra (ring theory) and algebra over a field.
• With a qualifier, there is the same distinction:
• Without article, it means a part of algebra, like linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves).
• With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra.
• Frequently both meanings exist for the same qualifier, like in the sentence: Commutative algebra is the study of commutative rings, that all arecommutative algebras over the integers.
• Sometimes "algebra" is also used to denote the operations and methods related to algebra in the study of a structure that does not belong to...