Calcula os seguintes produtos e somas
Monómios e polinómios: Matematicamente Falando 8 - Pág. 126 Ex. 2
Enunciado
Nos monómios seguintes, as variáveis designam-se por x, y e z.
Calcula os seguintes produtos e somas de monómios e apresenta-os na forma canónica.
| \(2{x^4} + 5{x^4}\) | \( – xy + 3xy\) | \(0,5xyz – \frac{1}{2}xyz\) | \(\frac{1}{2}{x^3} + 2{x^3}\) |
| \(\frac{1}{2}{x^2}y – \frac{5}{2}{x^2}y\) | \( – \frac{3}{5}{x^2} + \frac{2}{3}{x^2}\) | \(2yz + \frac{5}{3}yz\) | \(x \times 3{x^2}\) |
| \( – {x^2} \times 0,5x\) | \(2x \times 0,7xy\) | \( – \frac{2}{7}{x^3} \times \left( { – \frac{1}{5}{x^2}} \right)\) | \(\frac{1}{2}{x^3} \times 2{x^5}\) |
Resolução
| a) | \(2{x^4} + 5{x^4} = \left( {2 + 5} \right){x^4} = 7{x^4}\) |
| b) | \( – xy + 3xy = \left( { – 1 + 3} \right)xy = 2xy\) |
| c) | \(0,5xyz – \frac{1}{2}xyz = \left( {0,5 – \frac{1}{2}} \right)xyz = 0 \times xyz = 0\) |
| d) | \(\frac{1}{2}{x^3} + 2{x^3} = \left( {\frac{1}{2} + 2} \right){x^3} = \left( {\frac{1}{2} + \frac{4}{2}} \right){x^3} = \frac{5}{2}{x^3}\) |
| e) | \(\frac{1}{2}{x^2}y – \frac{5}{2}{x^2}y = \left( {\frac{1}{2} – \frac{5}{2}} \right){x^2}y = – 2{x^2}y\) |
| f) | \( – \frac{3}{{\mathop 5\limits_{\left( 3 \right)} }}{x^2} + \frac{2}{{\mathop 3\limits_{\left( 5 \right)} }}{x^2} = \left( { – \frac{9}{{15}} + \frac{{10}}{{15}}} \right){x^2} = \frac{1}{{15}}{x^2}\) |
| g) | \(2yz + \frac{5}{3}yz = \left( {\frac{6}{3} + \frac{5}{3}} \right)yz = \frac{{11}}{3}yz\) |
| h) | \(x \times 3{x^2} = \left( {1 \times 3} \right) \times \left( {x \times {x^2}} \right) = 3{x^3}\) |
| i) | \( – {x^2} \times 0,5x = \left( { – 1 \times 0,5} \right) \times \left( {{x^2} \times x} \right) = – 0,5{x^3}\) |
| j) | \(2x \times 0,7xy = \left( {2 \times 0,7} \right) \times \left( {x \times xy} \right) = 1,4{x^2}y\) |
| k) | \( – \frac{2}{7}{x^3} \times \left( { – \frac{1}{5}{x^2}} \right) = \left( { – \frac{2}{7} \times \left( { – \frac{1}{5}} \right)} \right) \times \left( {{x^3} \times {x^2}} \right) = \frac{2}{{35}}{x^5}\) |
| l) | \(\frac{1}{2}{x^3} \times 2{x^5} = \left( {\frac{1}{2} \times 2} \right) \times \left( {{x^3} \times {x^5}} \right) = {x^8}\) |
