Difference of Two Squares
Download as PPTX, PDF1 like1,008 views
This document provides instructions on factoring polynomials using the difference of two squares formula. It begins with the objectives and a review of perfect squares. It then presents the difference of two squares formula a2 - b2 = (a - b)(a + b) and provides examples of factoring expressions like x2 - 25 and 3x2 - 75 using this formula. The document stresses that for an expression to be factorable as a difference of two squares, it must be a binomial with two terms that are perfect squares separated by a subtraction sign. It provides a table for students to identify whether additional expressions can be factorized this way. In the conclusion, it summarizes the key things to remember about factoring the difference of
Difference of Two Squares
- 1. Factoring : Difference of Two Squares Lorie Jane L. Letada Module 1
- 2. Objectives At the end of this lesson, you are expected to: • identify expression factorable by difference of two squares; • factor difference of two squares completely.
- 3. Review Below is the list of the first 15 perfect square numbers. Can you give the answer of the last three?
- 4. What’s New Directions: Match the factors in column A with the products in column B. Write the letter before the number. You can use the FOIL method.
- 5. What is it Mastery on the perfect square of a number is very important in learning the new technique in factoring polynomials, which is the difference of two squares. Recall, (𝑦 − 2)(𝑦 + 2) = 𝑦2 − 4 by distributive property of multiplication or by FOIL method. This time you are going to do the reverse.
- 6. Difference of Two Squares - two terms that are squared and separated by a subtraction sign like this: 𝑎2 − 𝑏2 . It can be factored into 𝑎2 − 𝑏2 = (a − b)(a + b)
- 7. 1) It must be a binomial (have two terms). 2) Both terms must be perfect squares (meaning that you could take the square root and they would come out evenly. 3) There must be a subtraction/negative sign (not addition) in between them Conditions
- 8. Example 1 Factor 𝑥2 − 25 Step 1. Check for common factors. Step 2. Check the given if it satisfies the 3 conditions. 𝑥2 − 25 has no common factor Conditions: 1) It must be a binomial (have two terms). 2) Both terms must be perfect squares (meaning that you could take the square root and they would come out evenly. 3) There must be a subtraction/negative sign (not addition) in between them
- 9. Step 3. Find the square of the first term and the second term. 𝑥2 − 25 = 𝑥 2 − (5)2 Step 4. Follow the pattern: 𝑎2 − 𝑏2 = (a − b)(a + b) 𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 𝑥2 − 25 = (𝑥 − 5 ) (𝑥 + 5 )
- 10. Example 2 Factor 3𝑥2 − 75 Step 1. Check for common factors. Step 2. Check the given if it satisfies the 3 conditions. 𝟑𝒙 𝟐 = Conditions: 1) It must be a binomial (have two terms). 2) Both terms must be perfect squares (meaning that you could take the square root and they would come out evenly. 3) There must be a subtraction/negative sign (not addition) in between them 3 • x • x 𝟕𝟓 = 3 • 5 • 5 𝑮𝑪𝑭 = 𝟑 𝑺𝒐, 𝟑 (𝑥2 − 25)
- 11. Step 3. Find the square of the first term and the second term. 3(𝑥2 − 25) = 𝑥 2 − (5)2 Step 4. Follow the pattern: 𝑎2 − 𝑏2 = (a − b)(a + b) 𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 3 (𝑥2 − 25) = 3 (𝑥 − 5 )(𝑥 + 5 )
- 12. Activity 1.2 Complete Me Directions: Complete the table by identifying whether the following polynomials are factorable by the difference of two squares or not. Provide what is asked in each column. The first one is done for you.
- 13. What I need to remember • Difference of Two Squares - two terms that are squared and separated by a subtraction sign like this: 𝑎2 − 𝑏2, can be factored into 𝑎2 − 𝑏2 = (a − b)(a + b) • Difference of Two Squares can be factored only when it is a binomial and there is a minus sign in between the two terms.