Calcula
Monómios e polinómios: Matematicamente Falando 8 - Pág. 147 Ex. 10
Enunciado
Calcula:
| a) | \({\left( {x – 1} \right)^2}\) |
| b) | \({\left( {1 – x} \right)^2}\) |
| c) | \({\left( {\frac{{3y}}{2} + 1} \right)^2}\) |
| d) | \({\left( {4x – 3} \right)^2}\) |
| e) | \(\left( {2 – x} \right)\left( {2 + x} \right)\) |
| f) | \(\left( {2xy + \frac{1}{2}} \right)\left( {2xy – \frac{1}{2}} \right)\) |
| g) | \(\left( { – 1 + x} \right)\left( { – 1 – x} \right)\) |
| h) | \(\left( {2x + 1} \right)\left( { – 2x + 1} \right)\) |
Resolução
O cálculo está apresentado abaixo:
| a) | \[{\left( {x – 1} \right)^2} = {x^2} + 2 \times x \times \left( { – 1} \right) + {\left( { – 1} \right)^2} = {x^2} – 2x + 1\] |
| b) | \[{\left( {1 – x} \right)^2} = {1^2} + 2 \times 1 \times \left( { – x} \right) + {\left( { – x} \right)^2} = 1 – 2x + {x^2}\] |
| c) | \[{\left( {\frac{{3y}}{2} + 1} \right)^2} = {\left( {\frac{{3y}}{2}} \right)^2} + 2 \times \frac{{3y}}{2} \times 1 + {1^2} = \frac{9}{4}{y^2} + 3y + 1\] |
| d) | \[{\left( {4x – 3} \right)^2} = {\left( {4x} \right)^2} + 2 \times 4x \times \left( { – 3} \right) + {\left( { – 3} \right)^2} = 16{x^2} – 24x + 9\] |
| e) | \[\left( {2 – x} \right)\left( {2 + x} \right) = {2^2} – {x^2} = 4 – {x^2}\] |
| f) | \[\left( {2xy + \frac{1}{2}} \right)\left( {2xy – \frac{1}{2}} \right) = {\left( {2xy} \right)^2} – {\left( {\frac{1}{2}} \right)^2} = 4{x^2}{y^2} – \frac{1}{4}\] |
| g) | \[\left( { – 1 + x} \right)\left( { – 1 – x} \right) = {\left( { – 1} \right)^2} – {x^2} = 1 – {x^2}\] |
| h) | \[\left( {2x + 1} \right)\left( { – 2x + 1} \right) = – {\left( {2x} \right)^2} + {1^2} = 1 – 4{x^2}\] |
