Easy Algebra Step-by-Step

Index 241

Dependent variable, 197
Difference of two cubes, 102, 134, 136
Difference of two squares, 102, 134–135
Distance between two points in a plane, 176–177
Distributive property, 11
Division. See also Fractions
addition and, 59, 120
of algebraic fractions, 145–146
of complex fractions, 151
components of, 110
with exponents
fractions, 54–56
natural numbers, 47–48
negative numbers, 51–52, 120
one, 45
power of a quotient rule, 79
quotient rule for, 75–77, 81
zero, 49
by GCF, 139–143
of integers, 4
linear equation rules, 155
linear inequality rules, 159, 161
multiplication and, 120
of natural numbers, 1–2
negative numbers in, 29–30
in order of operations, 59–63, 68
of polynomials, 110 –117, 120
in polynomial expressions, 104–105
quotient rule for, 75–77, 81
sign for, 29
signed numbers rules, 29–30
simplifying, 120
of whole numbers, 2
zero in, 4, 29, 110, 139, 155, 180–181
Domain of functions, 195–200

e (transcendental number), 6, 8
Elimination method, 208–210
“Equal to” symbol (=), 120
Equations
linear. See Linear equations
quadratic. See Quadratic equations
sides of, 154
solving, 154
Exponents
defi nition of, 44
in exponential expression, 45f
fractions as, 53–57, 84–85
highest common, 121

natural numbers as, 44–48, 74–81

negative numbers as, 50–52, 77, 84–85,

104 –105, 120

one as, 45, 95

rational, 54–57

rules for, 74–81

zero as, 48–49

Exponential expression

components of, 45f

defi nition of, 44

parentheses in, 48, 59

power of a product rule, 78–80, 119–120

power of a quotient rule, 79

a power to a power rule, 77–78

product rule, 74–75

quotient rule, 75–77

reciprocals of, 50–51

Exponentiation

defi nition of, 44

in order of operations

with addition, 48, 120

algebraic expressions, 69

PEMDAS, 59–62

polynomial expressions, 106–108

Factors

“equal to” symbol and, 120

greatest common, 121–126, 139–143

prime, 148

vs. terms, 119

Factor ing

of algebraic fractions, 139–143

defi nition of, 119

by FOIL method, 127–131

by grouping, 126–127, 131–133

guidelines for, 137

with negative coeffi cients, 123–125

objective of, 119

one in, 122–126

perfect trinomial squares, 133–134

quadratic trinomials, 127–133

two terms, 134 –136

Fahrenheit to Celsius conversion, 70

Fifth root, 38

FOIL method, 99–101, 127–131

Fourth root, 6, 38

Fractions

absolute value of, 16–17

addition of, 19–20