{"id":1871,"date":"2021-12-02T19:39:49","date_gmt":"2021-12-03T00:39:49","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-6-5\/"},"modified":"2023-09-01T12:59:13","modified_gmt":"2023-09-01T16:59:13","slug":"answer-key-6-5","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-6-5\/","title":{"raw":"Answer Key 6.5","rendered":"Answer Key 6.5"},"content":{"raw":"
    \r\n \t
  1. [latex]6p-42[\/latex]<\/li>\r\n \t
  2. [latex]32k^2+16k[\/latex]<\/li>\r\n \t
  3. [latex]12x+6[\/latex]<\/li>\r\n \t
  4. [latex]18n^3+21n^2[\/latex]<\/li>\r\n \t
  5. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&8n&+&8&& \\\\\r\n\\times &4n&+&6&& \\\\\r\n\\hline\r\n&32n^2&+&32n&& \\\\\r\n&&&48n&+&48 \\\\\r\n\\hline\r\n&32n^2&+&80n&+&48\r\n\\end{array}[\/latex]<\/li>\r\n \t
  6. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&x&-&4&& \\\\\r\n\\times &2x&+&1&& \\\\\r\n\\hline\r\n&2x^2&-&8x&& \\\\\r\n&&&x&-&4 \\\\\r\n\\hline\r\n&2x^2&-&7x&-&4\r\n\\end{array}[\/latex]<\/li>\r\n \t
  7. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&7b&-&5&& \\\\\r\n\\times &8b&+&3&& \\\\\r\n\\hline\r\n&56b^2&-&40b&& \\\\\r\n&&+&21b&-&15 \\\\\r\n\\hline\r\n&56b^2&-&19b&-&15\r\n\\end{array}[\/latex]<\/li>\r\n \t
  8. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&4r&+&8&& \\\\\r\n\\times &r&+&8&& \\\\\r\n\\hline\r\n&4r^2&+&8r&& \\\\\r\n&&+&32r&+&64 \\\\\r\n\\hline\r\n&4r^2&+&40r&+&64\r\n\\end{array}[\/latex]<\/li>\r\n \t
  9. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&5v&-&2&& \\\\\r\n\\times &3v&-&4&& \\\\\r\n\\hline\r\n&15v^2&-&6v&& \\\\\r\n&&-&20v&+&8 \\\\\r\n\\hline\r\n&15v^2&-&26v&+&8\r\n\\end{array}[\/latex]<\/li>\r\n \t
  10. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&a&-&8&& \\\\\r\n\\times &6a&+&4&& \\\\\r\n\\hline\r\n&6a^2&-&48a&& \\\\\r\n&&+&4a&-&32 \\\\\r\n\\hline\r\n&6a^2&-&44a&-&32\r\n\\end{array}[\/latex]<\/li>\r\n \t
  11. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&6x&-&4y&& \\\\\r\n\\times &5x&+&y&& \\\\\r\n\\hline\r\n&30x^2&-&20xy&& \\\\\r\n&&+&6xy&-&4y^2 \\\\\r\n\\hline\r\n&30x^2&-&14xy&-&4y^2\r\n\\end{array}[\/latex]<\/li>\r\n \t
  12. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&8u&-&7v&& \\\\\r\n\\times &2u&+&3v&& \\\\\r\n\\hline\r\n&16u^2&-&14uv&& \\\\\r\n&&+&24uv&-&21v^2 \\\\\r\n\\hline\r\n&16u^2&+&10uv&-&21v^2\r\n\\end{array}[\/latex]<\/li>\r\n \t
  13. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&8x&+&3y&& \\\\\r\n\\times &7x&+&5y&& \\\\\r\n\\hline\r\n&56x^2&+&21xy&& \\\\\r\n&&+&40xy&+&15y^2 \\\\\r\n\\hline\r\n&56x^2&+&61xy&+&15y^2\r\n\\end{array}[\/latex]<\/li>\r\n \t
  14. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&a&-&3b&& \\\\\r\n\\times &5a&+&8b&& \\\\\r\n\\hline\r\n&5a^2&-&15ab&& \\\\\r\n&&+&8ab&-&24b^2 \\\\\r\n\\hline\r\n&5a^2&-&7ab&-&24b^2\r\n\\end{array}[\/latex]<\/li>\r\n \t
  15. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrr}\r\n&6r^2&-&r&+&5&& \\\\\r\n\\times &&&r&-&7&& \\\\\r\n\\hline\r\n&6r^3&-&r^2&+&5r&& \\\\\r\n&&-&42r^2&+&7r&-&35 \\\\\r\n\\hline\r\n&6r^3&-&43r^2&+&12r&-&35\r\n\\end{array}[\/latex]<\/li>\r\n \t
  16. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrr}\r\n&4x^2&+&3x&+&5&& \\\\\r\n\\times &&&4x&+&8&& \\\\\r\n\\hline\r\n&16x^3&+&12x^2&+&20x&& \\\\\r\n&&+&32x^2&+&24x&+&40 \\\\\r\n\\hline\r\n&16x^3&+&44x^2&+&44x&+&40\r\n\\end{array}[\/latex]<\/li>\r\n \t
  17. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrr}\r\n&2n^2&-&2n&+&5&& \\\\\r\n\\times &&&6n&-&4&& \\\\\r\n\\hline\r\n&12n^3&-&12n^2&+&30n&& \\\\\r\n&&-&8n^2&+&8n&-&20 \\\\\r\n\\hline\r\n&12n^3&-&20n^2&+&38n&-&20\r\n\\end{array}[\/latex]<\/li>\r\n \t
  18. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrr}\r\n&4b^2&+&4b&+&4&& \\\\\r\n\\times &&&2b&-&3&& \\\\\r\n\\hline\r\n&8b^3&+&8b^2&+&8b&& \\\\\r\n&&-&12b^2&-&12b&-&12 \\\\\r\n\\hline\r\n&8b^3&-&4b^2&-&4b&-&12\r\n\\end{array}[\/latex]<\/li>\r\n \t
  19. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrr}\r\n&6x^2&-&7xy&+&4y^2&& \\\\\r\n\\times &&&6x&+&3y&& \\\\\r\n\\hline\r\n&36x^3&-&42x^2y&+&24xy^2&& \\\\\r\n&&+&18x^2y&-&21xy^2&+&12y^3 \\\\\r\n\\hline\r\n&36x^3&-&24x^2y&+&3xy^2&+&12y^3\r\n\\end{array}[\/latex]<\/li>\r\n \t
  20. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrr}\r\n&7m^2&+&6mn&+&4n^2&& \\\\\r\n\\times &&&3m&-&2n&& \\\\\r\n\\hline\r\n&21m^3&+&18m^2n&+&12mn^2&& \\\\\r\n&&-&14m^2n&-&12mn^2&-&8n^3 \\\\\r\n\\hline\r\n&21m^3&+&4m^2n&-&8n^3&&\r\n\\end{array}[\/latex]<\/li>\r\n \t
  21. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrrrr}\r\n&6n^2&-&5n&+&6&&&& \\\\\r\n\\times&8n^2&+&4n&+&6&&&& \\\\\r\n\\hline\r\n&48n^4&-&40n^3&+&48n^2&&&& \\\\\r\n&&+&24n^3&-&20n^2&+&24n&& \\\\\r\n&&&&+&36n^2&-&30n&+&36 \\\\\r\n\\hline\r\n&48n^4&-&16n^3&+&64n^2&-&6n&+&36\r\n\\end{array}[\/latex]<\/li>\r\n \t
  22. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrrrr}\r\n&7a^2&-&6a&+&1&&&& \\\\\r\n\\times&2a^2&+&6a&+&3&&&& \\\\\r\n\\hline\r\n&14a^4&-&12a^3&+&2a^2&&&& \\\\\r\n&&+&42a^3&-&36a^2&+&6a&& \\\\\r\n&&&&+&21a^2&-&18a&+&3 \\\\\r\n\\hline\r\n&14a^4&+&30a^3&-&13a^2&-&12a&+&3\r\n\\end{array}[\/latex]<\/li>\r\n \t
  23. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrrrr}\r\n&3k^2&+&3k&+&6&&&& \\\\\r\n\\times&5k^2&+&3k&+&3&&&& \\\\\r\n\\hline\r\n&15k^4&+&15k^3&+&30k^2&&&& \\\\\r\n&&+&9k^3&+&9k^2&+&18k&& \\\\\r\n&&&&+&9k^2&+&9k&+&18 \\\\\r\n\\hline\r\n&15k^4&+&24k^3&+&48k^2&+&27k&+&18\r\n\\end{array}[\/latex]<\/li>\r\n \t
  24. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrrrr}\r\n&6u^2&+&4uv&+&3v^2&&&& \\\\\r\n\\times &7u^2&+&8uv&-&6v^2&&&& \\\\\r\n\\hline\r\n&42u^4&+&28u^3v&+&21u^2v^2&&&& \\\\\r\n&&+&48u^3v&+&32u^2v^2&+&24uv^3&& \\\\\r\n&&&&-&36u^2v^2&-&24uv^3&-&18v^4 \\\\\r\n\\hline\r\n&42u^4&+&76u^3v&+&17u^2v^2&-&18v^4&& \\\\\r\n\\end{array}[\/latex]<\/li>\r\n \t
  25. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrrrrrrrr}\r\n&2n^3&-&8n^2&+&3n&+&6&&&&&& \\\\\r\n\\times&n^3&-&6n^2&-&2n&+&3&&&&&& \\\\\r\n\\hline\r\n&2n^6&-&8n^5&+&3n^4&+&6n^3&&&&&& \\\\\r\n&&-&12n^5&+&48n^4&-&18n^3&-&36n^2&&&& \\\\\r\n&&&&-&4n^4&+&16n^3&-&6n^2&-&12n&& \\\\\r\n&&&&&&+&6n^3&-&24n^2&+&9n&+&18 \\\\\r\n\\hline\r\n&2n^6&-&20n^5&+&47n^4&+&10n^3&-&66n^2&-&3n&+&18\r\n\\end{array}[\/latex]<\/li>\r\n \t
  26. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrrrrrrrrrr}\r\n&a^3&+&2a^2&+&3a&+&3&&&&&& \\\\\r\n\\times&a^3&+&2a^2&-&4a&+&1&&&&&& \\\\\r\n\\hline\r\n&a^6&+&2a^5&+&3a^4&+&3a^3&&&&&& \\\\\r\n&&+&2a^5&+&4a^4&+&6a^3&+&6a^2&&&& \\\\\r\n&&&&-&4a^4&-&8a^3&-&12a^2&-&12a&& \\\\\r\n&&&&&&+&a^3&+&2a^2&+&3a&+&3 \\\\\r\n\\hline\r\n&a^6&+&4a^5&+&3a^4&+&2a^3&-&4a^2&-&9a&+&3\r\n\\end{array}[\/latex]<\/li>\r\n \t
  27. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&2x&+&1&& \\\\\r\n\\times &3x&-&4&& \\\\\r\n\\hline\r\n&6x^2&+&3x&& \\\\\r\n&&-&8x&-&4 \\\\\r\n\\hline\r\n&3(6x^2&-&5x&-&4) \\\\\r\n&18x^2&-&15x&-&12\r\n\\end{array}[\/latex]<\/li>\r\n \t
  28. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&2x&-&3&& \\\\\r\n\\times &x&-&4&& \\\\\r\n\\hline\r\n&2x^2&-&3x&& \\\\\r\n&&-&8x&+&12 \\\\\r\n\\hline\r\n&5(2x^2&-&11x&+&12) \\\\\r\n&10x^2&-&55x&+&60\r\n\\end{array}[\/latex]<\/li>\r\n \t
  29. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&4x&-&5&& \\\\\r\n\\times &2x&+&1&& \\\\\r\n\\hline\r\n&8x^2&-&10x&& \\\\\r\n&&+&4x&-&5 \\\\\r\n\\hline\r\n&3(8x^2&-&6x&-&5) \\\\\r\n&24x^2&-&18x&-&15\r\n\\end{array}[\/latex]<\/li>\r\n \t
  30. [latex]\\phantom{a}[\/latex]\r\n[latex]\\begin{array}[t]{rrrrrr}\r\n&2x&-&6&& \\\\\r\n\\times &4x&+&1&& \\\\\r\n\\hline\r\n&8x^2&-&24x&& \\\\\r\n&&+&2x&-&6 \\\\\r\n\\hline\r\n&2(8x^2&-&22x&-&6) \\\\\r\n&16x^2&-&44x&-&12\r\n\\end{array}[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]6p-42[\/latex]<\/li>\n
    2. [latex]32k^2+16k[\/latex]<\/li>\n
    3. [latex]12x+6[\/latex]<\/li>\n
    4. [latex]18n^3+21n^2[\/latex]<\/li>\n
    5. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &8n&+&8&& \\\\ \\times &4n&+&6&& \\\\ \\hline &32n^2&+&32n&& \\\\ &&&48n&+&48 \\\\ \\hline &32n^2&+&80n&+&48 \\end{array}[\/latex]<\/li>\n
    6. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &x&-&4&& \\\\ \\times &2x&+&1&& \\\\ \\hline &2x^2&-&8x&& \\\\ &&&x&-&4 \\\\ \\hline &2x^2&-&7x&-&4 \\end{array}[\/latex]<\/li>\n
    7. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &7b&-&5&& \\\\ \\times &8b&+&3&& \\\\ \\hline &56b^2&-&40b&& \\\\ &&+&21b&-&15 \\\\ \\hline &56b^2&-&19b&-&15 \\end{array}[\/latex]<\/li>\n
    8. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &4r&+&8&& \\\\ \\times &r&+&8&& \\\\ \\hline &4r^2&+&8r&& \\\\ &&+&32r&+&64 \\\\ \\hline &4r^2&+&40r&+&64 \\end{array}[\/latex]<\/li>\n
    9. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &5v&-&2&& \\\\ \\times &3v&-&4&& \\\\ \\hline &15v^2&-&6v&& \\\\ &&-&20v&+&8 \\\\ \\hline &15v^2&-&26v&+&8 \\end{array}[\/latex]<\/li>\n
    10. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &a&-&8&& \\\\ \\times &6a&+&4&& \\\\ \\hline &6a^2&-&48a&& \\\\ &&+&4a&-&32 \\\\ \\hline &6a^2&-&44a&-&32 \\end{array}[\/latex]<\/li>\n
    11. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &6x&-&4y&& \\\\ \\times &5x&+&y&& \\\\ \\hline &30x^2&-&20xy&& \\\\ &&+&6xy&-&4y^2 \\\\ \\hline &30x^2&-&14xy&-&4y^2 \\end{array}[\/latex]<\/li>\n
    12. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &8u&-&7v&& \\\\ \\times &2u&+&3v&& \\\\ \\hline &16u^2&-&14uv&& \\\\ &&+&24uv&-&21v^2 \\\\ \\hline &16u^2&+&10uv&-&21v^2 \\end{array}[\/latex]<\/li>\n
    13. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &8x&+&3y&& \\\\ \\times &7x&+&5y&& \\\\ \\hline &56x^2&+&21xy&& \\\\ &&+&40xy&+&15y^2 \\\\ \\hline &56x^2&+&61xy&+&15y^2 \\end{array}[\/latex]<\/li>\n
    14. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &a&-&3b&& \\\\ \\times &5a&+&8b&& \\\\ \\hline &5a^2&-&15ab&& \\\\ &&+&8ab&-&24b^2 \\\\ \\hline &5a^2&-&7ab&-&24b^2 \\end{array}[\/latex]<\/li>\n
    15. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrr} &6r^2&-&r&+&5&& \\\\ \\times &&&r&-&7&& \\\\ \\hline &6r^3&-&r^2&+&5r&& \\\\ &&-&42r^2&+&7r&-&35 \\\\ \\hline &6r^3&-&43r^2&+&12r&-&35 \\end{array}[\/latex]<\/li>\n
    16. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrr} &4x^2&+&3x&+&5&& \\\\ \\times &&&4x&+&8&& \\\\ \\hline &16x^3&+&12x^2&+&20x&& \\\\ &&+&32x^2&+&24x&+&40 \\\\ \\hline &16x^3&+&44x^2&+&44x&+&40 \\end{array}[\/latex]<\/li>\n
    17. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrr} &2n^2&-&2n&+&5&& \\\\ \\times &&&6n&-&4&& \\\\ \\hline &12n^3&-&12n^2&+&30n&& \\\\ &&-&8n^2&+&8n&-&20 \\\\ \\hline &12n^3&-&20n^2&+&38n&-&20 \\end{array}[\/latex]<\/li>\n
    18. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrr} &4b^2&+&4b&+&4&& \\\\ \\times &&&2b&-&3&& \\\\ \\hline &8b^3&+&8b^2&+&8b&& \\\\ &&-&12b^2&-&12b&-&12 \\\\ \\hline &8b^3&-&4b^2&-&4b&-&12 \\end{array}[\/latex]<\/li>\n
    19. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrr} &6x^2&-&7xy&+&4y^2&& \\\\ \\times &&&6x&+&3y&& \\\\ \\hline &36x^3&-&42x^2y&+&24xy^2&& \\\\ &&+&18x^2y&-&21xy^2&+&12y^3 \\\\ \\hline &36x^3&-&24x^2y&+&3xy^2&+&12y^3 \\end{array}[\/latex]<\/li>\n
    20. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrr} &7m^2&+&6mn&+&4n^2&& \\\\ \\times &&&3m&-&2n&& \\\\ \\hline &21m^3&+&18m^2n&+&12mn^2&& \\\\ &&-&14m^2n&-&12mn^2&-&8n^3 \\\\ \\hline &21m^3&+&4m^2n&-&8n^3&& \\end{array}[\/latex]<\/li>\n
    21. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrr} &6n^2&-&5n&+&6&&&& \\\\ \\times&8n^2&+&4n&+&6&&&& \\\\ \\hline &48n^4&-&40n^3&+&48n^2&&&& \\\\ &&+&24n^3&-&20n^2&+&24n&& \\\\ &&&&+&36n^2&-&30n&+&36 \\\\ \\hline &48n^4&-&16n^3&+&64n^2&-&6n&+&36 \\end{array}[\/latex]<\/li>\n
    22. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrr} &7a^2&-&6a&+&1&&&& \\\\ \\times&2a^2&+&6a&+&3&&&& \\\\ \\hline &14a^4&-&12a^3&+&2a^2&&&& \\\\ &&+&42a^3&-&36a^2&+&6a&& \\\\ &&&&+&21a^2&-&18a&+&3 \\\\ \\hline &14a^4&+&30a^3&-&13a^2&-&12a&+&3 \\end{array}[\/latex]<\/li>\n
    23. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrr} &3k^2&+&3k&+&6&&&& \\\\ \\times&5k^2&+&3k&+&3&&&& \\\\ \\hline &15k^4&+&15k^3&+&30k^2&&&& \\\\ &&+&9k^3&+&9k^2&+&18k&& \\\\ &&&&+&9k^2&+&9k&+&18 \\\\ \\hline &15k^4&+&24k^3&+&48k^2&+&27k&+&18 \\end{array}[\/latex]<\/li>\n
    24. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrr} &6u^2&+&4uv&+&3v^2&&&& \\\\ \\times &7u^2&+&8uv&-&6v^2&&&& \\\\ \\hline &42u^4&+&28u^3v&+&21u^2v^2&&&& \\\\ &&+&48u^3v&+&32u^2v^2&+&24uv^3&& \\\\ &&&&-&36u^2v^2&-&24uv^3&-&18v^4 \\\\ \\hline &42u^4&+&76u^3v&+&17u^2v^2&-&18v^4&& \\\\ \\end{array}[\/latex]<\/li>\n
    25. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrrrrr} &2n^3&-&8n^2&+&3n&+&6&&&&&& \\\\ \\times&n^3&-&6n^2&-&2n&+&3&&&&&& \\\\ \\hline &2n^6&-&8n^5&+&3n^4&+&6n^3&&&&&& \\\\ &&-&12n^5&+&48n^4&-&18n^3&-&36n^2&&&& \\\\ &&&&-&4n^4&+&16n^3&-&6n^2&-&12n&& \\\\ &&&&&&+&6n^3&-&24n^2&+&9n&+&18 \\\\ \\hline &2n^6&-&20n^5&+&47n^4&+&10n^3&-&66n^2&-&3n&+&18 \\end{array}[\/latex]<\/li>\n
    26. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrrrrrrrrrr} &a^3&+&2a^2&+&3a&+&3&&&&&& \\\\ \\times&a^3&+&2a^2&-&4a&+&1&&&&&& \\\\ \\hline &a^6&+&2a^5&+&3a^4&+&3a^3&&&&&& \\\\ &&+&2a^5&+&4a^4&+&6a^3&+&6a^2&&&& \\\\ &&&&-&4a^4&-&8a^3&-&12a^2&-&12a&& \\\\ &&&&&&+&a^3&+&2a^2&+&3a&+&3 \\\\ \\hline &a^6&+&4a^5&+&3a^4&+&2a^3&-&4a^2&-&9a&+&3 \\end{array}[\/latex]<\/li>\n
    27. [latex]\\phantom{a}[\/latex]
      \n[latex]\\begin{array}[t]{rrrrrr} &2x&+&1&& \\\\ \\times &3x&-&4&& \\\\ \\hline &6x^2&+&3x&& \\\\ &&-&8x&-&4 \\\\ \\hline &3(6x^2&-&5x&-&4) \\\\ &18x^2&-&15x&-&12 \\end{array}[\/latex]<\/li>\n
    28. [latex]\\phantom{a}[\/latex]
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