Calcula
Equações de grau superior ao 1.º: Matematicamente Falando 8 - Parte 2 Pág. 70 Ex. 15
Enunciado
Calcula:
- ${{(2x-3)}^{2}}$
- ${{(x+7)}^{2}}$
- ${{\left( y+\frac{1}{2} \right)}^{2}}$
- ${{(4a-3b)}^{2}}$
- ${{(-x-1)}^{2}}$
- ${{(x+1)}^{2}}$
Resolução
- Ora,
\[\begin{array}{*{35}{l}}
{{(2x-3)}^{2}} & = & {{(2x)}^{2}}+2\times 2x\times (-3)+{{(-3)}^{2}} \\
{} & = & 4{{x}^{2}}-12x+9 \\
\end{array}\] - Ora,
\[\begin{array}{*{35}{l}}
{{(x+7)}^{2}} & = & {{x}^{2}}+2\times x\times 7+{{7}^{2}} \\
{} & = & {{x}^{2}}+14x+49 \\
\end{array}\] - Ora,
\[\begin{array}{*{35}{l}}
{{\left( y+\frac{1}{2} \right)}^{2}} & = & {{y}^{2}}+2\times y\times \frac{1}{2}+{{(\frac{1}{2})}^{2}} \\
{} & = & {{y}^{2}}+y+\frac{1}{4} \\
\end{array}\] - Ora,
\[\begin{array}{*{35}{l}}
{{(4a-3b)}^{2}} & = & {{(4a)}^{2}}+2\times 4a\times (-3b)+{{(-3b)}^{2}} \\
{} & = & 16{{a}^{2}}-24ab+9{{b}^{2}} \\
\end{array}\] - Ora,
\[\begin{array}{*{35}{l}}
{{(-x-1)}^{2}} & = & {{(-x)}^{2}}+2\times (-x)\times (-1)+{{(-1)}^{2}} \\
{} & = & {{x}^{2}}+2x+1 \\
\end{array}\] - Ora,
\[\begin{array}{*{35}{l}}
{{(x+1)}^{2}} & = & {{x}^{2}}+2\times x\times 1+{{1}^{2}} \\
{} & = & {{x}^{2}}+2x+1 \\
\end{array}\]
