To Expand Expressions

• Place the cursor at the end of the expression, insert the symbolic evaluation operator, and type the keyword expand in the placeholder. PTC Mathcad expands the expression by multiplying out powers and products and by applying identities for common functions.

<region id="ID0EOH4JB" top="76.800000000000011" left="57.600000000000009" height="39.2" width="306.56666666666666" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="5">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <pow />
        <parens>
          <apply>
            <plus />
            <id xml:space="preserve">x</id>
            <id xml:space="preserve">y</id>
          </apply>
        </parens>
        <real>3</real>
      </apply>
      <command>
        <id xml:space="preserve">expand</id>
      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <plus />
            <apply>
              <plus />
              <apply>
                <pow />
                <id labels="*" xml:space="preserve">x</id>
                <real>3</real>
              </apply>
              <apply>
                <mult />
                <apply>
                  <mult />
                  <real>3</real>
                  <apply>
                    <pow />
                    <id labels="*" xml:space="preserve">x</id>
                    <real>2</real>
                  </apply>
                </apply>
                <id labels="*" xml:space="preserve">y</id>
              </apply>
            </apply>
            <apply>
              <mult />
              <apply>
                <mult />
                <real>3</real>
                <id labels="*" xml:space="preserve">x</id>
              </apply>
              <apply>
                <pow />
                <id labels="*" xml:space="preserve">y</id>
                <real>2</real>
              </apply>
            </apply>
          </apply>
          <apply>
            <pow />
            <id labels="*" xml:space="preserve">y</id>
            <real>3</real>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

<region id="ID0E5H4JB" top="134.40000000000003" left="57.600000000000009" height="39.2" width="245.09666666666669" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="7">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">sin</id>
        <apply>
          <mult />
          <real>2</real>
          <id xml:space="preserve">x</id>
        </apply>
      </apply>
      <command>
        <id xml:space="preserve">expand</id>
      </command>
      <symResult>
        <apply>
          <mult />
          <apply>
            <mult />
            <real>2</real>
            <apply>
              <id labels="FUNCTION" xml:space="preserve">cos</id>
              <id labels="*" xml:space="preserve">x</id>
            </apply>
          </apply>
          <apply>
            <id labels="FUNCTION" xml:space="preserve">sin</id>
            <id labels="*" xml:space="preserve">x</id>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

<region id="ID0ETJ4JB" top="192.00000000000003" left="57.600000000000009" height="39.2" width="355.12" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="9">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <apply>
        <mult />
        <parens>
          <apply>
            <plus />
            <id xml:space="preserve">x</id>
            <real>1</real>
          </apply>
        </parens>
        <parens>
          <apply>
            <plus />
            <id xml:space="preserve">y</id>
            <id xml:space="preserve">z</id>
          </apply>
        </parens>
      </apply>
      <command>
        <sequence>
          <id xml:space="preserve">expand</id>
          <parens>
            <apply>
              <plus />
              <id xml:space="preserve">x</id>
              <real>1</real>
            </apply>
          </parens>
        </sequence>
      </command>
      <symResult>
        <apply>
          <plus />
          <apply>
            <mult />
            <id labels="*" xml:space="preserve">y</id>
            <parens>
              <apply>
                <plus />
                <id labels="*" xml:space="preserve">x</id>
                <real>1</real>
              </apply>
            </parens>
          </apply>
          <apply>
            <mult />
            <id labels="*" xml:space="preserve">z</id>
            <parens>
              <apply>
                <plus />
                <id labels="*" xml:space="preserve">x</id>
                <real>1</real>
              </apply>
            </parens>
          </apply>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

• If the expression is a fraction, the numerator expands and the expression is written as a sum of fractions.

• Sines, cosines, and tangents of sums of variables, or integer multiples of variables, expand as far as possible into expressions involving only sines and cosines of single variables.

• If the expression cannot be expanded further, the expression is unchanged.