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| Algebraic
Expressions |
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Terms, variables, constants -
coefficients
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Monomial, binomial, trinomial, . . . , polynomial
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Simplifying algebraic
expressions |
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Like terms, collecting
or combining like terms |
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Evaluating algebraic expressions |
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| Terms, variables, constants -
coefficients
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| An
algebraic expression is one or more algebraic terms
containing variables and constants connected by mathematical
operations. |
| Terms
are the elements separated by the plus or minus signs. |
| In
algebraic expressions, variables are letters, such as a,
b, c,
or x,
y,
z,
that can have different values. |
| Constants
are the terms or elements represented only by numbers. |
| Coefficients
are the number part of the terms that multiply a variable or
powers of a variable. |
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| Example: |
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a2
- 6a
+ 5 -
is
the algebraic
expression of three terms, where a
is
the variable, 1 and
-
6 are
coefficients of the first term and of the middle
term a,
and
5 is the constant.
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| Monomial, binomial, trinomial, . . . polynomial
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| An
algebraic expression consisting of a single term is called a
monomial, expression consisting of two terms is binomial, three
terms trinomial and an expression with more than three terms is
called polynomial. |
| A
monomial is an expression consisting of a single term, such as -
2a3b. |
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| Examples: |
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- 3x2
and
2ab
are monomials, a3
- b3
is
the binomial, |
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x2
-
4x
+ 4 is
the trinomial, and
a3
- 3a2
+
3a
- 1
is the polynomial.
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| Simplifying algebraic
expressions |
| By
simplifying an algebraic expression, we mean reducing it in the
simplest possible form which mainly involves: multiplication
and division, removing (expanding) brackets and collecting (adding
and subtracting) like
terms. |
| Like
terms are those terms which contain the same powers of same
variables and which can only differ in coefficients. |
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| Examples: |
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a)
- 4a3
+
3a2
+
5a3
- 7a2
= (- 4
+
5)
· a3
+
(3 - 7)
· a2 = a3 - 4a2, |
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b)
(x2
- x
+
1)
·
(x
+
1) =
x3 - x2
+
x
+
x2
- x
+
1 = x3
+
1. |
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| Evaluating algebraic expressions |
| To
evaluate an algebraic expression means to replace (substitute)
the variables in the expression with numeric values that are
assigned to them and perform the operations in the expression. |
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| Example: |
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Evaluate
the expression x2
- 6xy
+
9y2
for x
= 2 and y
= -1. |
| Solution: |
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22 - 6
·
2
·
(- 1)
+
9
·
(-1)2
= 4 +
12 +
9 = 25. |
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| Beginning
Algebra Contents B |
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| Copyright
© 2004 - 2020, Nabla Ltd. All rights reserved. |
