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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!!!.

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Bellringer part two

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  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

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