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4.1E: Exercises

  • Page ID
    108349
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    Practice Makes Perfect

    Add and Subtract Polynomials

    In the following exercises, add or subtract the polynomials.

    1. \(4p+11p\)

    Answer

    \(15p\)

    2. \(−8y^3−5y^3\)

    Answer

    \(−13y^3\)

    3. \((4a^2+9a−11)+(6a^2−5a+10)\)

    Answer

    \(10a^2+4a-1\)

    4. \((8m^2+12m−5)−(2m^2−7m−1)\)

    Answer

    \(6m^2+19m−4\)

    5. \((y^2−3y+12)+(5y^2−9)\)

    Answer

    \(6y^2-3y+3\)

    6. \((5u^2+8u)−(4u−7)\)

    Answer

    \(5u^2+4u+7\)

    7. Find the sum of \(8q^3−27\) and \(q^2+6q−2\).

    Answer

    \(2x^2−2x+23\)

    8. Find the difference of \(x^2+6x+8\) and \(x^2−8x+15\).

    Answer

    \(14x-7\)

    In the following exercises, simplify.

    9. \(17mn^2−(−9mn^2)+3mn^2\)

    Answer

    \(29mn^2\)

    10. \(18a−7b−21a\)

    Answer

    \(−7b−3a\)

    11. \(2pq^2−5p−3q^2\)

    Answer

    \(2pq^2−5p−3q^2\)

    12. \((6a^2+7)+(2a^2−5a−9)\)

    Answer

    \(8a^2−5a−2\)

    13. \((3p^2−4p−9)+(5p^2+14)\)

    Answer

    \(8p^2-4p+5\)

    14. \((7m^2−2m−5)−(4m^2+m−8)\)

    Answer

    \(−3m-3m+3\)

    15. \((7b^2−4b+3)−(8b^2−5b−7)\)

    Answer

    \(-b^2-b-10\)

    16. Subtract \((8y^2−y+9)\) from \( (11y^2−9y−5) \)

    Answer

    \(3y^2−8y−14\)

    17. Find the difference of \((z^2−4z−12)\) and \((3z^2+2z−11)\)

    Answer

    \(-2z^2+6z+1\)

    18. \((x^3−x^2y)−(4xy^2−y^3)+(3x^2y−xy^2)\)

    Answer

    \(y^3-5xy^2+2x^2y+x^3\)

    19. \((x^3−2x^2y)−(xy^2−3y^3)−(x^2y−4xy^2)\)

    Answer

    \(3y^3+3xy^2-3x^2y+x^3\)

    Multiply Monomials

    In the following exercises, multiply the monomials.

    20. \((−6p^4)(9p)\)

    Answer

    \(-54p^{5}\)

    21. \(\left(\frac{1}{3}c^2\right)(30c^8)\)

    Answer

    \(10c^{10}\)

    22. \((8x^2y^5)(7xy^6)\)

    Answer

    \(56x^3y^{11}\)

    23. \( \left(\frac{2}{3}m^3n^6\right)\left(\frac{1}{6}m^4n^4\right)\)

    Answer

    \(\dfrac{m^7n^{10}}{9}\)

    Multiply a Polynomial by a Monomial

    In the following exercises, multiply.

    24. \(7(10−x)\)

    Answer

    \(70-7x\)

    25. \(a^2(a^2−9a−36)\)

    Answer

    \(a^4−9a^3−36a^2\)

    26. \(−5y(125y^3−1)\)

    Answer

    \(-625y^4+5y\)

    27. \((4n−5)(2n^3)\)

    Answer

    \(8n^4−10n^3\)

    Multiply a Binomial by a Binomial

    In the following exercises, multiply the binomials using any method:

    28. \((a+5)(a+2)\)

    Answer

    \(a^2+7a+10\)

    29. \((y−4)(y+12)\)

    Answer

    \(y^2+8y−48\)

    30. \((3x+1)(2x−7)\)

    Answer

    \(6x^2-19x-7\)

    31. \((6p−11)(3p−10)\)

    Answer

    \(18p^2−93p+110\)

    32. \((n+8)(n+1)\)

    Answer

    \(n^2+9n+8\)

    33. \((k+6)(k−9)\)

    Answer

    \(k^2−3k−54\)

    34. \((5u−3)(u+8)\)

    Answer

    \(5u^2+37u-24\)

    35. \((2y−9)(5y−7)\)

    Answer

    \(10y^2−59y+63\)

    36. \((p+4)(p+7)\)

    Answer

    \(p^2+11p+28\)

    37. \((x−8)(x+9)\)

    Answer

    \(x^2+x−72\)

    38. \((3c+1)(9c−4)\)

    Answer

    \(27c^2-3c-4\)

    39. \((10a−1)(3a−3)\)

    Answer

    \(30a^2−33a+3\)

    Multiply a Polynomial by a Polynomial

    In the following exercises, multiply using any method

    40. \((x+1)(x^2−3x−21)\)

    Answer

    \(x^3-2x^2-24x-21\)

    41. \((5b−2)(3b^2+b−9)\)

    Answer

    \(15b^3−b^2−47b+18\)

    42. \((m+6)(m^2−7m−30)\)

    Answer

    \(m^3-m^2-72m-180\)

    43. \((4y−1)(6y^2−12y+5)\)

    Answer

    \(24y^2−54y^2+32y−5\)

    Multiply Special Products

    In the following exercises, square each binomial using the Binomial Squares Pattern.

     

    44. \((x−3)^2\)

    Answer

    \(x^2 - 6x + 9\)

    45. \((x−5)^2\)

    Answer

    \(x^2 - 10x + 25\)

    46. \((x+1)^2\)

    Answer

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

    47. \((x+3)^2\)

    Answer

    \(x^2 + 6x + 9\)

    48. \((2x−y)^2\)

    Answer

    \(4x^2-4xy+y^2\)

    49. \((x+\dfrac{3}{4})^2\)

    Answer

    \(x^2+\dfrac{3}{2}x+\dfrac{9}{16}\)

    50. \((8p^3−3)^2\)

    Answer

    \(64p^6-48p^3+9\)

    51. \((5p+7q)^2\)

    Answer

    \(25p^2+70pq+49q^2\)

    In the following exercises, multiply each pair of conjugates using the Product of Conjugates.

     

    52. \((y+5)(y−5)\)

    Answer

    \(y^2−25\)

    53. \((x-4)(x+4)\)

    Answer

    \(x^2−16\)

    54. \((a+3)(a−3)\)

    Answer

    \(a^2−9\)

    55. \((m+1)(m-1)\)

    Answer

    \(m^2−1\)

    56. \((x+9)(x−9)\)

    Answer

    \(x^2-81\)

    57. \((3y+5)(3y−5)\)

    Answer

    \(9y^2−25\)

     

    58. \((6x+y)(6x−y)\)

    Answer

    \(36x^2−y^2\)

    59. \((a+\dfrac{2}{3}b)(a−\dfrac{2}{3}b)\)

    Answer

    \(a^2−\dfrac{4}{9}b^2\)

    60. \((12x^3−7y^2)(12x^3+7y^2)\)

    Answer

    \(144x^6−49y^4\)

    61. \((13a^2−8b4)(13a^2+8b^4)\)

    Answer

    \(169a^4-64b^8\)


    This page titled 4.1E: Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Stanislav A. Trunov and Elizabeth J. Hale via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.