Difference of Squares

Learn and apply difference of squares using equations, examples, and interpretation.

Lesson 2 of 53 parts Practice Flashcards

1/3

Recognizing Squares

Objective: Explain and use recognizing squares in an Algebra 1 problem.

A²−B² has two square terms separated by subtraction, with no middle term. No, the real difference-of-squares rule needs subtraction.

Worked examples

Try itExample 1.1: Factor x²−4. What is the positive root?Show answer

2. The real roots of a difference of squares are opposite values. The answer is 2.

Swipe sideways to move between sections

Recognizing Squares

Objective: Explain and use recognizing squares in an Algebra 1 problem.

A²−B² has two square terms separated by subtraction, with no middle term. No, the real difference-of-squares rule needs subtraction.

Worked examples

Try itExample 1.1: Factor x²−4. What is the positive root?Show answer

2. The real roots of a difference of squares are opposite values. The answer is 2.

Conjugate Factors

Objective: Explain and use conjugate factors in an Algebra 1 problem.

The identity A²−B²=(A−B)(A+B) follows because opposite cross-products cancel. AB and −AB cancel.

Worked examples

Try itExample 2.1: Factor x²−9. What is the positive root?Show answer

3. The real roots of a difference of squares are opposite values. The answer is 3.

Repeated Factoring

Objective: Explain and use repeated factoring in an Algebra 1 problem.

After using a difference of squares, inspect the resulting factors for another common factor or square difference. Further factors available over complex numbers may differ from real factors.

Worked examples

Try itExample 3.1: Factor x²−16. What is the positive root?Show answer

4. The real roots of a difference of squares are opposite values. The answer is 4.

You finished the reading!

Lock it in with a few practice questions, then move on to the next lesson.

Practice Next lesson

Previous lessonFactoring Trinomials Next lessonZero-Product Property