1 / 12

Factoring a Difference of Squares

Factoring a Difference of Squares. Essential Question. How do I factor binomials using difference of squares?. Give these a try. Multiply. 4(j + 6) (n – 9)(n + 9) (2t + 5)(2t + 5) Solutions: 4j + 24 n 2 –81 4t 2 +20t +25. Definition. Perfect Squares :

Download Presentation

Factoring a Difference of Squares

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Factoring a Difference of Squares

  2. Essential Question • How do I factor binomials using difference of squares?

  3. Give these a try • Multiply. • 4(j + 6) • (n – 9)(n + 9) • (2t + 5)(2t + 5) • Solutions: • 4j + 24 • n2 –81 • 4t2 +20t +25

  4. Definition • Perfect Squares: • What you get after you multiply something times itself. • For example: • 0, 1, 4, 9, 16, 25, etc. • Is x2 a perfect square? • What about x4y6z8? YES YES

  5. Difference of Squares • For all numbers a and b: a2 – b2 = (a + b)(a – b)

  6. Ex. 1) Factor 4a2 – 25b2 • First…ALWAYS try to factor out a GCF! • We can’t • Are both of these terms perfect squares? • Is there a minus sign in the middle? • Then use “difference of squares”. • (2a + 5b)(2a – 5b)

  7. Ex. 2) Factor 36x4 - 9y2 • Is there a GCF? • Yes • 9(4x4 – y2) • Are both terms left in the parentheses perfect squares? • Is there a minus sign between the terms? • Factor using a difference of squares! • 9(2x2 – y)(2x2 + y)

  8. Ex. 3) Factor -49 + a4 • First rewrite in standard form! • a4 – 49 • Now we can factor the difference of squares! • (a2 – 7)(a2 + 7)

  9. Ex. 4) Factor 16r2 + 49 • Is there a GCF? • NO …. • Are both terms perfect squares? • Yes • Is there a minus sign in the middle? • NO! • Can’t factor using difference of squares. • Must be PRIME

  10. Ex. 5) Factor 25n2 – 100 • What should you always ask yourself FIRST??? • GCF • 25 (n2 – 4) • 25(n + 2)(n – 2) • MUST DO GCF FIRST!!

  11. Ex. 6) Factor 16x2 – 49x4 • GCF??? YES! • x2(16-49x2) • x2(4-7x)(4+7x)

  12. Practice Factor Completely! • x2 – 4 • 36a2 – 49b2 • 25w2x4 – 81y2 • (x + 2)(x – 2) • (6a + 7b)(6a – 7b) • (5wx2 + 9y)(5wx2 – 9y)

More Related