{"id":10,"date":"2017-08-23T06:42:10","date_gmt":"2017-08-23T06:42:10","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/mathematics\/?page_id=10"},"modified":"2017-09-18T13:41:21","modified_gmt":"2017-09-18T13:41:21","slug":"algebraic-expressions","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/mathematics\/algebraic-expressions\/","title":{"rendered":"Algebraic Expressions"},"content":{"rendered":"
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\u2b05 Previous Lesson<\/a>\u00a0Workshop Index<\/a>\u00a0Next Lesson \u27a1<\/a><\/div>\n

<\/p>\n

Algebraic Expressions<\/h1>\n

Objective<\/h4>\n

In this lesson, you will study how to use operations to solve problems involving monomials, binomials, polynomials,\u00a0and algebraic fractions.<\/p>\n

\n

How do I add and subtract monomials?<\/h3>\n

You can add monomials if they are like terms. Like\u00a0terms<\/abbr> have the same variable raised to the same
\nexponent. For example,\u00a0.\u00a0Terms such as 4x<\/em> and 5y<\/em> cannot be added because they\u00a0have different variables. Terms such as 4x<\/em> and\u00a0\u00a0cannot be added either; even though they have the same variable,\u00a0it is raised to different powers.<\/p>\n

These same rules apply to subtraction of monomials.<\/p>\n

\n

Question<\/h4>\n
\n

Which choice shows the correct simplification of ?<\/p>\n

<\/p>\n

    \n
  1. <\/li>\n
  2. <\/li>\n
  3. <\/li>\n
  4. <\/li>\n<\/ol>\n

    <\/p>\n<\/div>\n

    Reveal Answer <\/a><\/p>\n

    \n

    The correct answer is D. To simplify the polynomial, combine\u00a0the like terms: 6xy<\/em> and 10xy<\/em> are like terms, so\u00a0.\u00a0Because 16xy<\/em> , 3x<\/em> , and 9y<\/em> are not like\u00a0terms, they cannot be combined. The polynomial simplifies to\u00a0.<\/p>\n<\/div>\n<\/section>\n

    How do I multiply and divide monomials?<\/h4>\n

    Monomials can be multiplied regardless of their variables and\u00a0exponents. Examples:\u00a0\u00a0and
    \n.\u00a0To do so, first multiply the numerical coefficients. Then, if variables have the same base, multiply them together by adding the\u00a0exponents. Division of monomials is done the same way, except the\u00a0exponents are subtracted.<\/p>\n

    \n

    Question<\/h4>\n
    \n

    Which choice shows the correct result of multiplying\u00a0?<\/p>\n

    <\/p>\n

      \n
    1. <\/li>\n
    2. <\/li>\n
    3. <\/li>\n
    4. <\/li>\n<\/ol>\n<\/div>\n

      Reveal Answer <\/a><\/p>\n

      \n

      The correct answer is A. To solve, multiply the coefficients,\u00a0multiply the variables, and then combine.<\/p>\n

      <\/p>\n<\/div>\n<\/section>\n

      How do I add and subtract binomials?<\/h4>\n

      To add binomials, combine like terms. For example,\u00a0.\u00a0Subtraction of binomials is done the same way.<\/p>\n

      \n

      Question<\/h4>\n
      \n

      Which choice shows the correct result of adding ?<\/p>\n

      <\/p>\n

        \n
      1. <\/li>\n
      2. <\/li>\n
      3. <\/li>\n
      4. <\/li>\n<\/ol>\n

        <\/p>\n<\/div>\n

        Reveal Answer <\/a><\/p>\n

        \n

        The correct answer is A. Combine the like terms. Because 4x\u00a0<\/em>and 3x<\/em> are like terms, add them together to get 7x<\/em>. 7x<\/em> , 2y<\/em> , and 7 are not like terms so the final\u00a0polynomial is\u00a0.<\/p>\n<\/div>\n<\/section>\n

        How do I multiply binomials?<\/strong><\/h3>\n

        One way to multiply binomials is to use the FOIL method. FOIL\u00a0stands for “f<\/strong>irst, o<\/strong>utside,\u00a0i<\/strong>nside, and l<\/strong>ast.”\u00a0For example,\u00a0\u00a0can be multiplied by the FOIL method.<\/p>\n

        The F in FOIL tells you to multiply the first term in each\u00a0binomial.<\/p>\n

        <\/p>\n

        The O in FOIL tells you to multiply the two outside terms.<\/p>\n

        <\/p>\n

        The I in FOIL tells you to multiply the two inside terms.<\/p>\n

        <\/center>The L in FOIL tells you to multiply the last two terms in each\u00a0binomial.<\/p>\n

        <\/p>\n

        Then add these terms together by combining like terms.<\/p>\n

        <\/p>\n

        \n

        Question<\/h4>\n
        \n

        Which choice shows the correct result of multiplying\u00a0?<\/p>\n

        <\/p>\n

          \n
        1. <\/li>\n
        2. <\/li>\n
        3. <\/li>\n
        4. <\/li>\n<\/ol>\n

          <\/p>\n<\/div>\n

          Reveal Answer <\/a><\/p>\n

          \n

          The correct answer is C. Use the FOIL method to solve.<\/p>\n

          <\/p>\n<\/div>\n<\/section>\n

          How do I multiply polynomials?<\/h4>\n

          To multiply polynomials, multiply each term in the first\u00a0polynomial by each term in the second polynomial, and then combine\u00a0like terms. For example,<\/p>\n

          <\/center><\/p>\n
          \n

          Question<\/h4>\n

          Which choice shows the correct result of multiplying\u00a0?<\/p>\n

          <\/p>\n

            \n
          1. <\/li>\n
          2. <\/li>\n
          3. <\/li>\n
          4. <\/li>\n<\/ol>\n

            <\/p>\n

            Reveal Answer <\/a><\/p>\n

            \n

            The correct answer is B. Multiply each term in the first\u00a0polynomial by each term in the second polynomial, and then\u00a0combine like terms.<\/p>\n

            <\/p>\n<\/div>\n<\/section>\n

            How do I simplify an algebraic fraction?<\/h4>\n

            To simplify an algebraic fraction, factor both the numerator\u00a0and denominator and then cross out like terms. For example,<\/p>\n

            <\/p>\n

            \n

            Question<\/h4>\n
            \n

            Which choice shows the correct simplification of\u00a0?<\/p>\n

            <\/p>\n

              \n
            1. <\/li>\n
            2. <\/li>\n
            3. <\/li>\n
            4. <\/li>\n<\/ol>\n<\/div>\n

              Reveal Answer <\/a><\/p>\n

              \n

              The correct answer is A. Factor the numerator and denominator\u00a0and then simplify.<\/p>\n

              <\/p>\n<\/div>\n<\/section>\n<\/section>\n

              <\/p>\n

              \u2b05 Previous Lesson<\/a>\u00a0Workshop Index<\/a>\u00a0Next Lesson \u27a1<\/a><\/div>\n

              Back to Top<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

              \u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Lesson \u27a1 Algebraic Expressions Objective In this lesson, you will study how to use operations to solve problems involving monomials, binomials, polynomials,\u00a0and algebraic fractions. How do I add and subtract monomials? You can add monomials if they are like terms. Like\u00a0terms have the same variable raised to the same exponent. For […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-10","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/10","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/comments?post=10"}],"version-history":[{"count":9,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/10\/revisions"}],"predecessor-version":[{"id":716,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/10\/revisions\/716"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/media?parent=10"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}