1 / 23

Bellringer part two

Bellringer part two. Simplify (m – 4) 2 . (5n + 3) 2. Determine the pattern. = 1 2 = 2 2 = 3 2 = 4 2 = 5 2 = 6 2. These are perfect squares ! You should be able to list at least the first 15 perfect squares in 30 seconds…. 1 4 9 16 25 36 …. GO!!!.

williamss
Download Presentation

Bellringer part two

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. Bellringer part two • Simplify • (m – 4)2. • (5n + 3)2.

  2. Determine the pattern = 12 = 22 = 32 = 42 = 52 = 62 These are perfect squares! You should be able to list at least the first 15 perfect squares in 30 seconds… 1 4 9 16 25 36 …

  3. GO!!! • Perfect squares1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225 How far did you get?

  4. Perfect Square Trinomial Ax2 + Bx + C • Clue 1: A & C are positive, perfect squares. • Clue 2: B is the square root of A times the square root of C, doubled. If these two things are true, the trinomial is a Perfect Square Trinomial and can be factored as (x + y)2 or (x – y)2.

  5. General Form of Perfect Square Trinomials • x2 + 2xy + y2 = (x + y)2 or • x2 – 2xy + y2 = (x - y)2 • Note: When factoring, the sign in the binomial is the same as the sign of B in the trinomial.

  6. Ex) x2 + 12x + 36 What’s the square root of A? of C? Multiply these and double. Does it = B? Then it’s a Perfect Square Trinomial! Solution: (x + 6)2 Ex) 16a2 – 56a + 49 Square root of A? of C? Multiply and double… = B? Solution: (4a – 7) 2 Just watch and think.

  7. 1. y² + 8y + 16 2. 9y² - 30y + 10 Ex. 1: Determine whether each trinomial is a perfect square trinomial. If so, factor it.

  8. 1) x2 + 8x + 16 2) 9n2 + 48n + 64 3) 4z2 – 36z + 81 4) 9g² +12g - 4 Example 2: Factoring perfect square trinomials.

  9. 25x² - 30x + 9 x² + 6x - 9 6) 49y² + 42y + 36 7) 9m³ + 66m² - 48m

  10. First terms: Outer terms: Inner terms: Last terms: Combine like terms. x2 – 4 Review: Multiply (x – 2)(x + 2) Notice the middle terms eliminate each other! x2 +2x -2x x2 -2x -4 +2x -4 This is called the difference of squares.

  11. Difference of Squares a2 - b2 = (a - b)(a + b)or a2 - b2 = (a + b)(a - b) The order does not matter!!

  12. 4 Steps for factoringDifference of Squares 1. Are there only 2 terms? 2. Is the first term a perfect square? 3. Is the last term a perfect square? 4. Is there subtraction (difference) in the problem? If all of these are true, you can factor using this method!!!

  13. No 1. Factor x2 - 25 x2 – 25 Yes When factoring, use your factoring table. Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? Write your answer! Yes Yes - Yes ( )( ) x + 5 x 5

  14. No 2. Factor 16x2 - 9 16x2 – 9 Yes When factoring, use your factoring table. Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? Write your answer! Yes Yes - Yes (4x )(4x ) + 3 3

  15. No 3. Factor 81a2 – 49b2 81a2 – 49b2 Yes When factoring, use your factoring table. Do you have a GCF? Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? Write your answer! Yes Yes - Yes (9a )(9a ) 7b 7b +

  16. Factor x2 – y2 • (x + y)(x + y) • (x – y)(x + y) • (x + y)(x – y) • (x – y)(x – y) Remember, the order doesn’t matter!

  17. Yes! GCF = 3 4. Factor 75x2 – 12 Yes 3(25x2 – 4) When factoring, use your factoring table. Do you have a GCF? 3(25x2 – 4) Are the Difference of Squares steps true? Two terms? 1st term a perfect square? 2nd term a perfect square? Subtraction? Write your answer! Yes Yes Yes - 3(5x )(5x ) 2 2 +

  18. Factor 18c2 + 8d2 • prime • 2(9c2 + 4d2) • 2(3c – 2d)(3c + 2d) • 2(3c + 2d)(3c + 2d) You cannot factor using difference of squares because there is no subtraction!

  19. Factor -64 + 4m2 • prime • (2m – 8)(2m + 8) • 4(-16 + m2) • 4(m – 4)(m + 4) Rewrite the problem as 4m2 – 64 so the subtraction is in the middle!

  20. 2x² + 18 c² - 5c + 6 5a³ - 80a 8x² - 18x - 35 Ex. 3: Factor completely.

  21. 3x² + 24x + 48 = 0 49a² + 16 = 56a Ex. 3: Solve each equation.

  22. z² + 2x + 1= 16 (y – 8)² = 7

More Related