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Factoring Using Difference of Squares

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Learn to factor using the difference of squares method with this helpful chart and practice exercises. Master the process step by step and enhance your algebra skills quickly!

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Factoring Using Difference of Squares

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  1. ObjectiveThe student will be able to: factor using difference of squares. SOL: A.2c

  2. Factoring ChartThis chart will help you to determine which method of factoring to use.TypeNumber of Terms 1. GCF 2 or more 2. Difference of Squares 2

  3. Determine the pattern = 12 = 22 = 32 = 42 = 52 = 62 These are perfect squares! You should be able to list the first 15 perfect squares in 30 seconds… 1 4 9 16 25 36 … Perfect squares1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

  4. 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.

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

  6. 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!!!

  7. 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

  8. 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

  9. 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 +

  10. 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!

  11. 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 +

  12. 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!

  13. 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!

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