Algebra Tutorials!  
Saturday 25th of February
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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Monomial Factors

The first thing you should know before factoring an algebraic expression is to identify any factors which are monomials.

Let's see what this is all about in the following example.


Remove all common monomial factors from 42b 2y – 28by 2.


This example is very similar to the previous one, and so you should try it as a practice problem on your own first, before looking at our brief outline of a solution. First, write out the factorization of each of the two terms explicitly:

42b 2y = 2 · 3 · 7 · b 2 · y 1


28by 2 = 2 2 · 7 · b 1 · y 2

Notice that we’ve written exponents of symbols explicitly, even if those exponents are 1 (just as a visual cue when we check now for common factors between the two terms). It is also helpful to sort the factors of the individual terms in a common order. Here numerical prime factors are sorted from smallest to largest (going left to right) and symbolic factors are sorted alphabetically.

Comparison of these two factorizations indicates immediately that the common factors are 2, 7, b, and y, all to the first power. Thus

42b 2y – 28by 2 = 2 · 7 · b · y (3b – 2y)

= 14by (3b – 2y).

The terms in the expression in brackets on the right here are obtained by taking what’s left of each of the original terms when the common factors are removed. Thus, since

42b 2y = 2 · 3 · 7 · b 2 · y 1

when we remove the factors 2, 7, b 1 , and y 1, all that’s left is the 3 and one of the factors b, or 3b. A similar inspection indicates that after removal of these four common factors from 28by 2, all that is left is the factors 2 and y, each to the first power.

Thus, the required factorization here is

42b 2y – 28by 2 = 14by (3b – 2y).

We’ll leave it up to you to verify that this is correct by multiplication.

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