How to Factor the Difference between Two Perfect Squares?
The technique of factoring the difference between two perfect squares is used when you want to factor a polynomial that involves the subtraction of two perfect squares. In this step-by-step guide, you will learn more about this technique!
Factor the Difference between Two Perfect Squares: what to notice and how to work it
What to notice first
Common student mistake
Key formulas and cues
A reliable path
- Organize by degreeWrite terms from highest power to lowest power.
- Look for structureTry GCF, special products, grouping, or division depending on the expression.
- Check with featuresZeros, multiplicity, and end behavior should agree with your algebra.
Worked examples
Combine like terms
- Group x squared terms.
- Group x terms.
- Combine each group.
Factor a difference of squares
- Recognize a squared term minus a squared term.
- Use a^2 – b^2.
- Write conjugate factors.
Try one before moving on
Factor the Difference between Two Perfect Squares: pop-up practice
A step-by-step guide to factoring the difference between two perfect squares
Factoring the difference between two squares is a special case of factoring a polynomial, where you factor a binomial, which is the difference between two terms that are both perfect squares.
Writing a binomial as the difference between two squares simply means that you rewrite a binomial as the product of two sets of parentheses. For example, \(a^2−b^2 =(a+b)(a−b)\). The binomial \(a^2−b^2\) can be factored into two sets of parentheses multiplied by each other. \((a+b)(a−b)\) will produce \(a^2−b^2\) when multiplied.
Not all terms can be factored in using this method. There are several clues to look for when determining whether an expression can be factored using the difference of squares. In the previous example, a2-b2, each term is a perfect square, and there is a subtraction symbol between each term. These are two useful clues to look for when determining whether a binomial can be factored using the difference between two squares. If these two clues exist, the expression can be factored using the difference of squares.
Factoring the Difference between Two Perfect Squares – Example 1:
Factor the following binomial using the difference of two squares method. \((x^2-81)\)
Solution:
The expression \((x^2-81)\) can be factored using the difference of two squares because both expressions are perfect squares and the expressions are separated by a subtraction sign. \(x^2\) is \(x\) times \(x\) and \(81\) is \(9\) times \(9\). \((x^2-81)\) can be rewritten as the product of \((x+9)(x-9)\).
Exercises for Factoring the Difference between Two Perfect Squares
Factor each polynomial using the difference of two squares method.
- \(\color{blue}{(64-x^2)}\)
- \(\color{blue}{(49x^2-25y^2)}\)
- \(\color{blue}{(625\:m^4-36y^2)}\)
- \(\color{blue}{(4x^4-144y^2)}\)
- \(\color{blue}{(8+x)(8-x)}\)
- \(\color{blue}{\left(7x+5y\right)\left(7x-5y\right)}\)
- \(\color{blue}{\left(25m^2+6y\right)\left(25m^2-6y\right)}\)
- \(\color{blue}{4\left(x^2+6y\right)\left(x^2-6y\right)}\)
Related to This Article
More math articles
- The Best Grade 8 Math Book for New Mexico Students
- Black Codes and the Civil Rights Act of 1866
- 8th Grade Georgia Milestones Assessment System Math FREE Sample Practice Questions
- Free Grade 4 English Worksheets for Georgia Students
- Obscenity
- Horse-race coverage
- Full-Length ISEE Upper Level Math Practice Test
- The Best Grade 7 ELA Practice Tests for Georgia Students
- Mastering the Midpoint & Distance on the Number Line
- How to Divide Polynomials Using Synthetic Division?
What people say about "How to Factor the Difference between Two Perfect Squares? - Effortless Math"?
No one replied yet.