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Difference of Two Squares

Difference of Two Squares. 7. 8. 9. 676. 729. 784. 841. 6. 3. 57. 58. 59. 60. 196. 4. 100. 484. 36. 324. 225. 121. 9. 361. 529. 49. 576. 256. 64. 400. 16. 144. 81. 169. 289. 441. 625. 25. 49. 50. 51. 52. 41. 42. 43. 44. 45. 46. 47. 48. 33. 34.

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Difference of Two Squares

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  1. Difference of Two Squares

  2. 7 8 9 676 729 784 841 6 3 57 58 59 60 196 4 100 484 36 324 225 121 9 361 529 49 576 256 64 400 16 144 81 169 289 441 625 25 49 50 51 52 41 42 43 44 45 46 47 48 33 34 35 36 4 3 4 5 25 26 27 28 29 30 31 32 1 1 2 2 17 18 19 20 9 10 11 12 21 53 37 13 61 38 54 62 22 14 23 15 55 63 39 40 56 16 24 64 1 5 6 2 7 3 8 4 A perfect square is a number whose product comes from a number multiplied with itself. 3 blocks 1 8 blocks

  3. 49 is a perfect square because 361 is a perfect square because 2.25 is a perfect square because 0.01 is a perfect square because is a perfect square because 48 is NOT a perfect square because 10 is NOT a perfect square because 2.24 is NOT a perfect square because A perfect square is a number that has a rational square root.

  4. x2 is a perfect square because a6 is a perfect square because z16 is a perfect square because A variable perfect square is a variable that has a square root. This happens whenever the exponent attached to the variable is even. x is a NOT perfect square because its exponent is odd x3 is a NOT perfect square because its exponent is odd x9 is a NOT perfect square because its exponent is odd

  5. We can combine the concepts of perfect square numbers with perfect square variables.

  6. Recognizing perfect squares is a very important element when factoring using Difference of 2 Squares. However, there are two other distinguishing features both of which are indicated in the title. Differenceof2Squares - terms must be perfect squares. - must involve subtraction. In essence both terms must have opposite signs (one positive and the other negative). - there must be two terms. No more. No less. EXAMPLE: 25x2 - 49 - Both terms are perfect squares. - Terms are being subtracted. - There are two terms.

  7. 4p2 – 9q2 _______ • 100 – a6 _______ • x2 – 9x _______ • a10 – 10 _______ • t100 – 100 _______ • 2m2 – 50 _______ • -121s4 + 196p8 _______ • d9 – 49e16 _______ • y6 – 1 _______ • _______ • 16p2 + 9q2 _______ • –a2 – 36 _______ The trickiest thing about this method is the recognition factor. All three elements must be verified before the expression is factored using Difference of 2 Squares. Identify whether the following polynomials can be factored using Difference of 2 Squares or not. For those that can’t be factored using Difference of 2 Squares what prevents it from being factored that way?

  8. After it is determined that an expression can be factored using Difference of 2 Squares, all that is left is to determine what the factors actually are. The factors of this kind of polynomial will be a binomial with its conjugate. The binomial is basically the sum of the square roots of each term. The conjugate is therefore the difference of the square roots of each term. EXAMPLE: 25x2 - 49 =(5x + 7) (5x - 7) To verify: (5x + 7) (5x - 7) = 25x2 -35x + 35x - 49 = 25x2- 49

  9. 4p2 – 9q2 • 100 – a6 • x2 – 9x • a10 – 10 • t100 – 100 • 2m2 – 50 • -121s4 + 196p8 • d9 – 49e16 • y6 – 1 • 16p2 + 9q2 • –a2 – 36 = (2p + 3q)(2p – 3q) = (10 + a3)(10 – a3) = x(x – 9) Can not be factored because 10 is not a perfert square. = (t50 + 10)(t50 – 10) = 2(m2 - 25) = 2(m + 5)(m – 5) = 196p8 – 121s4 = (14p4 + 11s2)(14p4 - 11s2) Can not be factored because d9 is not a perfert square. = (y3 + 1)(y3 – 1) Can not factor SUM of 2 Squares = -1(a2 + 36) Can not factor SUM of 2 Squares

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