Algebra Tutorials!
Tuesday 20th of March
 Home Exponential Decay Negative Exponents Multiplying and Dividing Fractions 4 Evaluating Expressions Involving Fractions The Cartesian Coordinate System Adding and Subtracting Fractions with Like Denominators Solving Absolute Value Inequalities Multiplying Special Polynomials FOIL Method Inequalities Solving Systems of Equations by Graphing Graphing Compound Inequalities Solving Quadratic Equations by Completing the Square Addition Property of Equality Square Roots Adding and Subtracting Fractions The Distance Formula Graphing Logarithmic Functions Fractions Dividing Mixed Numbers Evaluating Polynomials Power of a Product Property of Exponents Terminology of Algebraic Expressions Adding and Subtracting Rational Expressions with Identical Denominators Solving Exponential Equations Factoring The Difference of 2 Squares Changing Fractions to Decimals Solving Linear Equations Using Patterns to Multiply Two Binomials Completing the Square Roots of Complex Numbers Methods for Solving Quadratic Equations Conics in Standard Form Solving Quadratic Equations by Using the Quadratic Formula Simplifying Fractions 2 Exponential Notation Exponential Growth The Cartesian Plane Graphing Linear Functions The Slope of a Line Finding Cube Roots of Large Numbers Rotating Axes Common Mistakes With Percents Solving an Equation That Contains a Square Root Rational Equations Properties of Common Logs Composition of Functions Using Percent Equations Solving Inequalities Properties of Exponents Graphing Quadratic Functions Factoring a Polynomial by Finding the GCF The Rectangular Coordinate System Adding and Subtracting Fractions Multiplying and Dividing Rational Expressions Improper Fractions and Mixed Numbers Properties of Exponents Complex Solutions of Quadratic Equations Solving Nonlinear Equations by Factoring Solving Quadratic Equations by Factoring Least Common Multiples http: Solving Exponential Equations Solving Linear Equations Multiplication Property of Equality Multiplying Mixed Numbers Multiplying Fractions Reducing a Rational Expression to Lowest Terms Literal Numbers Factoring Trinomials Logarithmic Functions Adding Fractions with Unlike Denominators Simplifying Square Roots Adding Fractions Equations Quadratic in Form Dividing Rational Expressions Slopes of Parallel Lines Simplifying Cube Roots That Contain Variables Functions and Graphs Complex Numbers Multiplying and Dividing Fractions 1 Composition of Functions Intercepts of a Line Powers http: Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10 Factoring Trinomials Exponents and Polynomials Decimals and their Equivalent Fractions Negative Integer Exponents Adding and Subtracting Mixed Numbers Solving Quadratic Equations Theorem of Pythagoras Equations 1 Subtracting Fractions Solving Quadratic Equations by Graphing Evaluating Polynomials Slope Angles and Degree Measure
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Factoring The Difference of 2 Squares

After studying this lesson, you will be able to:

• Factor the difference of two squares.

Steps of Factoring:

1. Factor out the GCF

2. Look at the number of terms:

• 2 Terms: Look for the Difference of 2 Squares
• 3 Terms: Factor the Trinomial
• 4 Terms: Factor by Grouping

3. Factor Completely

4. Check by Multiplying

This lesson will concentrate on the second step of factoring: Factoring the Difference of 2 Squares.

**When there are 2 terms, we look for the difference of 2 squares. Don't forget to look for a GCF first.**

We have the difference of two squares when the following are true:

There are 2 terms separated by a minus sign

To factor the difference of 2 squares, we write 2 parentheses. One will have an addition sign and the other will have a subtraction sign like this:

Next, we find the square root of the first term. We put these in the first positions. Then, we find the square root of the constant term and we put these in the last positions.

Example 1

Factor

There is no GCF other than one. This is the difference of two squares. Now we take the square root of the first term. The square root of Â¼ x 2 is so we put in the first positions:

Now we take the square root of the constant term. The square root of is y so we put in the last positions. Now, the problem is completely factored.

Check by using FOIL

Example 2

Factor 12x 3 - 27xy 2

There is a GCF in this problem. Therefore, we have to factor out the GCF first. The GCF is 3x so we factor that out.

3x (4x 2 - 9y 2)

Now we have the difference of two squares remaining in the parentheses. We have to factor completely so we factor the difference of two squares.....keeping the GCF.

3x (2x + 3y ) (2x - 3y )

Check (it will take two steps to check) First forget about the 3x for the time being and FOIL the 2 binomials:

(2x + 3y) (2x - 3y) 4x 2 - 6xy + 6xy - 9y 2 which is 4x 2 - 9y 2

Now multiply the result by 3x:

3x (4x 2 - 9y 2) 12x 3 - 27xy 2

Example 3

Factor 162x 4 - 32y8

There is a GCF in this problem. Therefore, we have to factor out the GCF first. The GCF is 2 so we factor that out.

2(81x 4 - 16y8 )

Now we have the difference of two squares remaining in the parentheses. We have to factor completely so we factor the difference of two squares.....keeping the GCF.

2(9x 2 + 4y4 ) (9x 2 - 4y4 )

The second parenthesis still contains the difference of 2 squares so we have to factor that again. We keep the GCF and the first parenthesis.

2(9x 2 + 4y4 ) (3x + 2y ) (3x - 2y )

This is now factored completely.

Check (it will take three steps to check) First forget about the 2 and the first binomial for the time being and FOIL the last 2 binomials:

(3x + 2y ) (3x - 2y ) (9x 2 - 4y4 )

Now multiply the 2 remaining binomials:

(9x 2 + 4y4 ) (9x 2 - 4y4 ) (81x 4 - 16y8 )

Now multiply the result by 2:

2(81x 4 - 16y8 ) 162x 4 - 32y8

 Copyrights © 2005-2018