C784 Algebra ON Constants, Variables, and Expressions Explained | Accurate & Verified Answers to Pass Actual Exam

C784 Algebra ON Constants, Variables, and Expressions Explained | Accurate & Verified Answers to

Pass Actual Exam


C784 ALGEBRA & FORWARD
Constants
Aconstant*is a number with a fixed value. All real numbers are constants,
including0,1.5,-10, andπ. Any of the numbers we used in "Number
Systems" are constants.
Variables
Avariable*is a symbol that represents or holds the place of a numerical
value. Often, a variable will be a letter from the Roman alphabet (a,b,c, … )
or Greek alphabet (α, β, γ, … ). The actual letter or symbol being used as a
variable is not important. The numerical value represented by the symbol is
what gives the variable its importance.
Exponents
Anexponent*, sometimes called a power, is a quantity that represents
repeated multiplication.
An exponent is written above and to the right of a number, known as a base.
The exponent's value is equal to the number of times the base is multiplied
by itself. In the example below, the base is6, and the exponent is3.
63is equal to6∗6∗6.




MULTIPLYING

Writing variables and numbers next to one another indicates multiplication.

2xmeans2∗x. This can be read as "2timesx."
3xymeans3∗x∗y. This can be read as "3timesxtimesy."
15xy2means15∗x∗y∗y. This can be read as
"15timesxtimesytimesy."

Only multiplication is denoted by numbers and variables being next to one
another with no written operation. Other operations like addition,
subtraction, and division require their corresponding operators.

In algebra,constants*often take the form ofcoefÏcients*. A coefÏcient is
a number by which a variable is being multiplied. CoefÏcients are written in
front of variables. So, in16x,16is the coefÏcient, andxis the variable.

,If a variable is without a number in front of it, the coefÏcient is1.
Though it is not written, there is essentially aninvisible1in front of any
variable without a numerical coefÏcient.
One of the fundamental building blocks of algebra is a term. Aterm*can be
many things, including a single constant (such as5), a single variable (such
asx), or any number of constants and variables multiplied together (such
as7ab).




Constant and coefÏcient:15
Variables:aandb
Exponent:2

Thedegree*of an expression is the highest power of the variable.

Example #3:9m4−2z2
Degree:4
In this expression,mmhas an exponent of4, andzhas an exponent of2.
The degree of an expression is equal to thelargest exponent, so the
degree here is4.
Example #4:12
Degree:0
In this expression, the degree is0because the constant can be imagined as
having an implied variable with an exponent of0:
12=12x0
Analgebraic expression*is a set of terms containing numbers, variables,
and operations.




Term 1 is8x2

,Term 2 is16xy
Term 3 is−12
It is standard to write expressions in descending order of exponent value
with constants at the end of the expression.

For example:y3−4x−51.

As we've learned, acoefÏcient*is aconstant*written in front of a
variable. A coefÏcient is written next to, specifically in front of, a variable
because it is being multiplied by that variable.
In a term, anexponent*is written as a superscript, above and to the right
of a variable. Exponents represent how many times a number or variable is
to be multiplied by itself, as opposed toadded to itself.




The term on the left,3x, has acoefÏcient of23. The term on the right,x3,
has anexponent of23.
Substitution*is a method used in algebra when a variable is substituted by
its known value. After performing substitution, we can evaluate the
expression like any other.

Tip:When substituting a value for a variable, it is a good idea to enclose the
value within parentheses. Using parentheses is a good visual way to keep
track of values that have replaced variables. This process is outlined below:

To combine like terms, we first need to identify which terms qualify as "like
terms." For terms to belike terms*, they need to have the same variable(s)
with the same exponent(s). As a reminder, aterm*is composed of a
constant multiplied by variable(s) and their exponent(s).

, Unlike terms:7xand7y
Don't be confused by the matching coefÏcients! Here, the terms
have two different variables once coefÏcients are
removed:xxandyy. The variables do not match, so these
arenotlike terms.
Unlike terms:3mand7m2
Be careful! Here, the terms have the same variable,m, but with
different exponents. Once coefÏcients are removed, we are left
withmandm2. While these may appear similar, the fact that the
variables have different exponents ensures that they arenotlike
terms.
Remember:Like terms always haveidentical variables with
identical exponents. Terms that have similar but slightly
different variables are not like terms and cannot be combined.
Similarly, terms that have the same variables but slightly different
exponents on those variables are not like terms and cannot be
combined.
While combining like terms is a way of
simplifyingexpressions*byaddingandsubtractingterms, the
distributive property deals with simplifying expressions
bymultiplyingterms.
Recall thatterms*include constants and variables being multiplied by one
another. So, when you multiply constants and variables, you end up with a
term.