Skip to main content
Global

6.4E: Mazoezi

  1. Last updated
  2. Save as PDF
  • Page ID
    176149

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Mazoezi hufanya kamili

    Factor Perfect Square trinomials

    Katika mazoezi yafuatayo, factor kabisa kutumia kamili mraba trinomials mfano.

    1. \(16y^2+24y+9\)

    Jibu

    \((4y+3)^2\)

    2. \(25v^2+20v+4\)

    3. \(36s^2+84s+49\)

    Jibu

    \((6s+7)^2\)

    4. \(49s^2+154s+121\)

    5. \(100x^2−20x+1\)

    Jibu

    \((10x−1)^2\)

    6. \(64z^2−16z+1\)

    7. \(25n^2−120n+144\)

    Jibu

    \((5n−12)^2\)

    8. \(4p^2−52p+169\)

    9. \(49x^2+28xy+4y^2\)

    Jibu

    \((7x+2y)^2\)

    10. \(25r^2+60rs+36s^2\)

    11. \(100y^2−52y+1\)

    Jibu

    \((50y−1)(2y−1)\)

    12. \(64m^2−34m+1\)

    13. \(10jk^2+80jk+160j\)

    Jibu

    \(10j(k+4)^2\)

    14. \(64x^2y−96xy+36y\)

    15. \(75u^4−30u^3v+3u^2v^2\)

    Jibu

    \(3u^2(5u−v)^2\)

    16. \(90p^4+300p^4q+250p^2q^2\)

    Tofauti za Mraba

    Katika mazoezi yafuatayo, sababu kabisa kutumia tofauti ya muundo wa mraba, ikiwa inawezekana.

    17. \(25v^2−1\)

    Jibu

    \((5v−1)(5v+1)\)

    18. \(169q^2−1\)

    19. \(4−49x^2\)

    Jibu

    \((7x−2)(7x+2)\)

    20. \(121−25s^2\)

    21. \(6p^2q^2−54p^2\)

    Jibu

    \(6p^2(q−3)(q+3)\)

    22. \(98r^3−72r\)

    23. \(24p^2+54\)

    Jibu

    \(6(4p^2+9)\)

    24. \(20b^2+140\)

    25. \(121x^2−144y^2\)

    Jibu

    \((11x−12y)(11x+12y)\)

    26. \(49x^2−81y^2\)

    27. \(169c^2−36d^2\)

    Jibu

    \((13c−6d)(13c+6d)\)

    28. \(36p^2−49q^2\)

    29. \(16z^4−1\)

    Jibu

    \((2z−1)(2z+1)(4z^2+1)\)

    30. \(m^4−n^4\)

    31. \(162a^4b^2−32b^2\)

    Jibu

    \(2b^2(3a−2)(3a+2)(9a^2+4)\)

    32. \(48m^4n^2−243n^2\)

    33. \(x^2−16x+64−y^2\)

    Jibu

    \((x−8−y)(x−8+y)\)

    34. \(p^2+14p+49−q^2\)

    35. \(a^2+6a+9−9b^2\)

    Jibu

    \((a+3−3b)(a+3+3b)\)

    36. \(m^2−6m+9−16n^2\)

    Kiasi cha Kiasi na Tofauti za Cubes

    Katika mazoezi yafuatayo, sababu kabisa kutumia kiasi na tofauti za muundo wa cubes, ikiwa inawezekana.

    37. \(x^3+125\)

    Jibu

    \((x+5)(x^2−5x+25)\)

    38. \(n^6+512\)

    39. \(z^6−27\)

    Jibu

    \((z^2−3)(z^4+3z^2+9)\)

    40. \(v^3−216\)

    41. \(8−343t^3\)

    Jibu

    \((2−7t)(4+14t+49t^2)\)

    42. \(125−27w^3\)

    43. \(8y^3−125z^3\)

    Jibu

    \((2y−5z)(4y^2+10yz+25z^2)\)

    44. \(27x^3−64y^3\)

    45. \(216a^3+125b^3\)

    Jibu

    \((6a+5b)(36a^2−30ab+25b^2)\)

    46. \(27y^3+8z^3\)

    47. \(7k^3+56\)

    Jibu

    \(7(k+2)(k^2−2k+4)\)

    48. \(6x^3−48y^3\)

    49. \(2x^2−16x^2y^3\)

    Jibu

    \(2x^2(1−2y)(1+2y+4y^2)\)

    50. \(−2x^3y^2−16y^5\)

    51. \((x+3)^3+8x^3\)

    Jibu

    \(9(x+1)(x^2+3)\)

    52. \((x+4)^3−27x^3\)

    53. \((y−5)^3−64y^3\)

    Jibu

    \(−(3y+5)(21y^2−30y+25)\)

    54. \((y−5)^3+125y^3\)

    Mazoezi ya mchanganyiko

    Katika mazoezi yafuatayo, factor kabisa.

    55. \(64a^2−25\)

    Jibu

    \((8a−5)(8a+5)\)

    56. \(121x^2−144\)

    57. \(27q^2−3\)

    Jibu

    \(3(3q−1)(3q+1)\)

    58. \(4p^2−100\)

    59. \(16x^2−72x+81\)

    Jibu

    \((4x−9)^2\)

    60. \(36y^2+12y+1\)

    61. \(8p^2+2\)

    Jibu

    \(2(4p^2+1)\)

    62. \(81x^2+169\)

    63. \(125−8y^3\)

    Jibu

    \((5−2y)(25+10y+4y^2)\)

    64. \(27u^3+1000\)

    65. \(45n^2+60n+20\)

    Jibu

    \(5(3n+2)^2\)

    66. \(48q^3−24q^2+3q\)

    67. \(x^2−10x+25−y^2\)

    Jibu

    \((x+y−5)(x−y−5)\)

    68. \(x^2+12x+36−y^2\)

    69. \((x+1)^3+8x^3\)

    Jibu

    \((3x+1)(3x^2+1)\)

    70. \((y−3)^3−64y^3\)

    Mazoezi ya kuandika

    71. Kwa nini ilikuwa muhimu kufanya mazoezi kwa kutumia muundo wa mraba wa binomial katika sura ya kuzidisha polynomials?

    Jibu

    Majibu yatatofautiana.

    72. Je, unatambua muundo wa mraba wa binomial?

    73. Eleza kwa nini\(n^2+25\neq (n+5)^2\). Tumia algebra, maneno, au picha.

    Jibu

    Majibu yatatofautiana.

    74. Maribel\(y^2−30y+81\) ilisababisha kama\((y−9)^2\). Je, yeye ni sahihi au makosa? Unajuaje?

    Self Check

    Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Jedwali hili lina safu 4 safu 3 na mstari wa kichwa. Mstari wa kichwa huandika kila safu ninayoweza, kwa ujasiri, kwa msaada na hapana, siipati. Safu ya kwanza ina kauli zifuatazo: kipengele cha trinomials kamili za mraba, tofauti za mraba, kiasi cha sababu na tofauti za cubes. Nguzo zilizobaki ni tupu.

    b Orodha hii inakuambia nini kuhusu ujuzi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?