Algebra Tutorials!  
Friday 19th of July
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
The Square of a Binomial
Factoring Trinomials
The Pythagorean Theorem
Solving Radical Equations in One Variable
Multiplying Binomials Using the FOIL Method
Imaginary Numbers
Solving Quadratic Equations Using the Quadratic Formula
Solving Quadratic Equations
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
Use of Parentheses or Brackets (The Distributive Law)
Multiplying and Dividing by Monomials
Solving Quadratic Equations by Graphing
Multiplying Decimals
Use of Parentheses or Brackets (The Distributive Law)
Simplifying Complex Fractions 1
Adding Fractions
Simplifying Complex Fractions
Solutions to Linear Equations in Two Variables
Quadratic Expressions Completing Squares
Dividing Radical Expressions
Rise and Run
Graphing Exponential Functions
Multiplying by a Monomial
The Cartesian Coordinate System
Writing the Terms of a Polynomial in Descending Order
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
Intercepts of a Line
Completing the Square
Order of Operations
Factoring Trinomials
Solving Linear Equations
Solving Multi-Step Inequalities
Solving Quadratic Equations Graphically and Algebraically
Collecting Like Terms
Solving Equations with Radicals and Exponents
Percent of Change
Powers of ten (Scientific Notation)
Comparing Integers on a Number Line
Solving Systems of Equations Using Substitution
Factoring Out the Greatest Common Factor
Families of Functions
Monomial Factors
Multiplying and Dividing Complex Numbers
Properties of Exponents
Multiplying Square Roots
Adding or Subtracting Rational Expressions with Different Denominators
Expressions with Variables as Exponents
The Quadratic Formula
Writing a Quadratic with Given Solutions
Simplifying Square Roots
Adding and Subtracting Square Roots
Adding and Subtracting Rational Expressions
Combining Like Radical Terms
Solving Systems of Equations Using Substitution
Dividing Polynomials
Graphing Functions
Product of a Sum and a Difference
Solving First Degree Inequalities
Solving Equations with Radicals and Exponents
Roots and Powers
Multiplying Numbers
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An expression such as 9p is a term; the number 9 is the coefficient, p is the variable, and 4 is the exponent. The expression pmeans p . p . p . p while p means p . p and so on. Terms having the same variable and the same exponent, such as 9x and -3x are like terms. Terms that do not have both the same variable and the same exponent, such as m and m are unlike terms. A polynomial is a term or a finite sum of terms in which all variables have whole number exponents, and no variables appear in denominators. Examples of polynomials include

5x + 2x + 6x, 8m + 9mn - 6mn + 3n, 10 p, and -9

Adding and Subtracting Polynomials

The following properties of real numbers are useful for performing operations on polynomials.


For all real numbers a, b, and c,

1. Commutative properties:

a + b = b + a

ab = ba

2. Associative properties

(a + b) + c = a + (b + c)

(ab)c = a(bc)

3. Distributive property

a(b + c) = ab + ac


Properties of Real Numbers

(a) 2 + x = x + 2 Commutative property of addition

(b) x.3 = 3x Commutative property of multiplication

(c) (7x)x = 7(x.x) = 7x Associative property of multiplication

(d) 3(x + 4) = 3x + 12 Distributive property

The distributive property is used to add or subtract polynomials. Only like terms may be added or subtracted. For example,

12y + 6y = (12 + 6)y = 18y


-2m + 8m = (-2 + 8)m = 6m

but the polynomial 8y + 2y cannot be further simplified. To subtract polynomials, use the facts that -(a+b)=-a-b and -(a-b)=-a+b In the next example, we show how to add and subtract polynomials.


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