Completa
Monómios e polinómios: Matematicamente Falando 8 - Pág. 136 Ex. 5
Enunciado
Completa:
| a) | \(\left( { \ldots + \ldots } \right)\left( {2x – \ldots } \right) = \ldots – 9\) |
| b) | \(\left( {4a + \ldots } \right)\left( { \ldots – \ldots } \right) = 16{a^2} – 25\) |
| c) | \(\left( { \ldots – x} \right)\left( { \ldots + \ldots } \right) = 4 – {x^2}\) |
| d) | \({\left( {y + 3} \right)^2} = \ldots + \ldots + \ldots \) |
| e) | \({\left( {x + \ldots } \right)^2} = \ldots + \ldots + 16\) |
| f) | \(\left( { \ldots + \frac{1}{2}} \right)\left( { \ldots – \frac{1}{2}} \right) = \frac{1}{9}{y^2} – \ldots \) |
| g) | \(\left( {z – 3} \right)\left( {z + 3} \right) = \ldots – \ldots \) |
| h) | \(\left( {n + \ldots } \right)\left( { \ldots – \ldots } \right) = \ldots – 25\) |
| i) | \({\left( {3x + \ldots } \right)^2} = \ldots + 12x + \ldots \) |
| j) | \({\left( {3x + \ldots } \right)^2} = \ldots + 6x + 1\) |
Resolução
As expressões completadas estão na coluna da direita.
| a) | \(\left( { \ldots + \ldots } \right)\left( {2x – \ldots } \right) = \ldots – 9\) | \(\left( {2x + 3} \right)\left( {2x – 3} \right) = 4{x^2} – 9\) |
| b) | \(\left( {4a + \ldots } \right)\left( { \ldots – \ldots } \right) = 16{a^2} – 25\) | \(\left( {4a + 5} \right)\left( {4a – 5} \right) = 16{a^2} – 25\) |
| c) | \(\left( { \ldots – x} \right)\left( { \ldots + \ldots } \right) = 4 – {x^2}\) | \(\left( {2 – x} \right)\left( {2 + x} \right) = 4 – {x^2}\) |
| d) | \({\left( {y + 3} \right)^2} = \ldots + \ldots + \ldots \) | \({\left( {y + 3} \right)^2} = {y^2} + 6y + 9\) |
| e) | \({\left( {x + \ldots } \right)^2} = \ldots + \ldots + 16\) | \({\left( {x + 4} \right)^2} = {x^2} + 8x + 16\) |
| f) | \(\left( { \ldots + \frac{1}{2}} \right)\left( { \ldots – \frac{1}{2}} \right) = \frac{1}{9}{y^2} – \ldots \) | \(\left( {\frac{1}{3}y + \frac{1}{2}} \right)\left( {\frac{1}{3}y – \frac{1}{2}} \right) = \frac{1}{9}{y^2} – \frac{1}{4}\) |
| g) | \(\left( {z – 3} \right)\left( {z + 3} \right) = \ldots – \ldots \) | \(\left( {z – 3} \right)\left( {z + 3} \right) = {z^2} – 9\) |
| h) | \(\left( {n + \ldots } \right)\left( { \ldots – \ldots } \right) = \ldots – 25\) | \(\left( {n + 5} \right)\left( {n – 5} \right) = {n^2} – 25\) |
| i) | \({\left( {3x + \ldots } \right)^2} = \ldots + 12x + \ldots \) | \({\left( {3x + 2} \right)^2} = 9{x^2} + 12x + 4\) |
| j) | \({\left( {3x + \ldots } \right)^2} = \ldots + 6x + 1\) | \({\left( {3x + 1} \right)^2} = 9{x^2} + 6x + 1\) |
