Calcula
Equações de grau superior ao 1.º: Matematicamente Falando 8 - Parte 2 Pág. 71 Ex. 17
Enunciado
Calcula:
- $(x+5)(x-5)$
- $(2x-1)(2x+1)$
- $(1-x)(1+x)$
- $(1-\frac{1}{2}x)(1+\frac{1}{2}x)$
- $(4xy-3)(4xy+3)$
Resolução
- Ora,
\[\begin{array}{*{35}{l}}
(x+5)(x-5) & = & {{x}^{2}}-{{5}^{2}} \\
{} & = & {{x}^{2}}-25 \\
\end{array}\] - Ora,
\[\begin{array}{*{35}{l}}
(2x-1)(2x+1) & = & {{(2x)}^{2}}-{{1}^{2}} \\
{} & = & 4{{x}^{2}}-1 \\
\end{array}\] - Ora,
\[\begin{array}{*{35}{l}}
(1-x)(1+x) & = & {{1}^{2}}-{{x}^{2}} \\
{} & = & 1-{{x}^{2}} \\
\end{array}\] - Ora,
\[\begin{array}{*{35}{l}}
(1-\frac{1}{2}x)(1+\frac{1}{2}x) & = & {{1}^{2}}-{{(\frac{1}{2}x)}^{2}} \\
{} & = & 1-\frac{1}{4}{{x}^{2}} \\
\end{array}\] - Ora,
\[\begin{array}{*{35}{l}}
(4xy-3)(4xy+3) & = & {{(4xy)}^{2}}-{{3}^{2}} \\
{} & = & 16{{x}^{2}}{{y}^{2}}-9 \\
\end{array}\]
