Calcula e simplifica

1. Ora,
   \[\begin{array}{*{35}{l}}
   2x({{x}^{2}}+3x-\frac{1}{2}) & = & 2x\times {{x}^{2}}+2x\times 3x+2x\times (-\frac{1}{2})  \\
   {} & = & 2{{x}^{3}}+6{{x}^{2}}-x  \\
   \end{array}\]
2. Ora,
   \[\begin{array}{*{35}{l}}
   -3x(-x+4) & = & -3x\times (-x)-3x\times 4  \\
   {} & = & 3{{x}^{2}}-12x  \\
   \end{array}\]
3. Ora,
   \[\begin{array}{*{35}{l}}
   ({{x}^{2}}-7x)\times \frac{{{x}^{3}}}{2} & = & {{x}^{2}}\times \frac{{{x}^{3}}}{2}-7x\times \frac{{{x}^{3}}}{2}  \\
   {} & = & \frac{{{x}^{5}}}{2}-\frac{7{{x}^{4}}}{2}  \\
   \end{array}\]
4. Ora,
   \[\begin{array}{*{35}{l}}
   (n-2)(n+3) & = & n\times n+n\times 3-2\times n-2\times 3  \\
   {} & = & {{n}^{2}}+3n-2n-6  \\
   {} & = & {{n}^{2}}+n-6  \\
   \end{array}\]
5. Ora,
   \[\begin{array}{*{35}{l}}
   (3a-1)({{a}^{2}}+\frac{1}{4}) & = & 3a\times {{a}^{2}}+3a\times \frac{1}{4}-1\times {{a}^{2}}-1\times \frac{1}{4}  \\
   {} & = & 3{{a}^{3}}+\frac{3}{4}a-{{a}^{2}}-\frac{1}{4}  \\
   {} & = & 3{{a}^{3}}-{{a}^{2}}+\frac{3}{4}a-\frac{1}{4}  \\
   \end{array}\]
6. Ora,
   \[\begin{array}{*{35}{l}}
   (1-m-{{m}^{2}})(m+2) & = & 1\times m+1\times 2-m\times m-m\times 2-{{m}^{2}}\times m-{{m}^{2}}\times 2  \\
   {} & = & m+2-{{m}^{2}}-2m-{{m}^{3}}-2{{m}^{2}}  \\
   {} & = & -{{m}^{3}}-3{{m}^{2}}-m+2  \\
   \end{array}\]
7. Ora,
   \[\begin{array}{*{35}{l}}
   (\frac{a}{2}-3)({{a}^{2}}-6a) & = & \frac{a}{2}\times {{a}^{2}}+\frac{a}{2}\times (-6a)-3\times {{a}^{2}}-3\times (-6a)  \\
   {} & = & \frac{{{a}^{3}}}{2}-3{{a}^{2}}-3{{a}^{2}}+18a  \\
   {} & = & \frac{{{a}^{3}}}{2}-6{{a}^{2}}+18a  \\
   \end{array}\]

Nota: Com a prática, a primeira passagem, em cada uma das alíneas, tenderá a ser omitida.