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Scientific Notation
Degree of a Polynomial
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Quadratic Equations with Imaginary Solutions
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Prime and Composite Numbers
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Linear Equations and Inequalities in One Variable
Notes on the Difference of 2 Squares
Solving Absolute Value Inequalities
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Using Slopes to Graph Lines
Fractions, Decimals and Percents
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Quotient Rule for Radicals
Prime Polynomials
Solving Nonlinear Equations by Substitution
Simplifying Radical Expressions Containing One Term
Factoring a Sum or Difference of Two Cubes
Finding the Least Common Denominator of Rational Expressions
Multiplying Rational Expressions
Expansion of a Product of Binomials
Solving Equations
Exponential Growth
Factoring by Grouping
Solving One-Step Equations Using Models
Solving Quadratic Equations by Factoring
Adding and Subtracting Polynomials
Rationalizing the Denominator
Rounding Off
The Distributive Property
What is a Quadratic Equation
Laws of Exponents and Multiplying Monomials
The Slope of a Line
Factoring Trinomials by Grouping
Multiplying and Dividing Rational Expressions
Solving Linear Inequalities
Multiplication Property of Exponents
Multiplying and Dividing Fractions 3
Dividing Monomials
Multiplying Polynomials
Adding and Subtracting Functions
Dividing Polynomials
Absolute Value and Distance
Multiplication and Division with Mixed Numbers
Factoring a Polynomial by Finding the GCF
Adding and Subtracting Polynomials
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Polar Form of a Complex Number
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Invariants Under Rotation
The Addition Method
Solving Linear Inequalities in One Variable
The Pythagorean Theorem
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Linear Equations and Inequalities in One Variable

English Words Math Symbols

(2 - moved)

2 + 3 = 3 + 2

2 · 3 = 3 · 2


(3 - grouped)

(2 + 3) + 5 = 2 + (3 + 5)

(2 · 3) · 5 = 2 · (3 · 5)


(multiplication over sum)

2 (3 + 5) = 2 · 3 + 2 · 5

(result = original)

2 + (0) = 2

3 · (1) = 3


(result = identity element)

2 + (- 2) = 0


Rule of Thumb for signed numbers:

Remember that the sign goes with the number that follows it.


Simplifying Expressions

Definition: Two or more terms with the same variable part are called Similar (or Liike) Terms.

Example 1:

Similar (or Liike) Terms:

Example 2:

Simplify each expression (Combine Liike Terms):

a) 7x2 - 2x2

7x2 - 2x2 = (7 - 2)x2 Distributive property
  = 5x2 Addition

b) 5y + 3x – 10y + 8x

5y + 3x – 10y + 8x = 5y – 10y + 3x + 8x Commutative property
  = (5y – 10y) + (3x + 8x) Associative property
  = (5 – 10)y + (3 + 8)x Distributive property
  = - 5y + 11x Addition:

Note: These terms cannot be combined because x ≠ y and the terms are not like or not similar.

Since there are fewer terms in the result than the beginning expression the result is simpler.



Apply the associative property to rewrite each of the following expressions, and then simplify when possible.

1. (5x + 3) + 4 = 5x + (3 + 4) Associative Property
  = 5x + 7 Addition
2. 7+ (4 + y) = (7 + 4) + y Associative Property
  = 11 + y Addition

The most often missed property is the distributive property. When there is a number or variable multiplied times an expression in parentheses, you must always make sure to multiply times each term inside the parentheses and stop with the "close paren".

Remember that the sign goes with the number that follows it.

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